NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties Of Solids

Access premium articles, webinars, resources to make the best decisions for career, course, exams, scholarships, study abroad and much more with

Plan, Prepare & Make the Best Career Choices

# NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties Of Solids

Edited By Vishal kumar | Updated on Sep 05, 2023 09:00 AM IST

## NCERT Solutions Class 11 Physics Chapter 9 – Free PDF Download

NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties Of Solids is an invaluable resource that aids students in comprehending the topics and preparing effectively for their exams. class 11 Physics Chapter 9 exercise solutions chapter consists of a total of twenty-one questions, each of which is explained in great detail and in a straightforward manner in Class 11 Physics Ch 9 NCERT solutions. It is crucial to take comprehensive notes while studying each topic. Solving textbook questions and gaining a strong grasp of the subject matter are equally vital. The experienced faculty has meticulously crafted the NCERT solutions in alignment with the latest CBSE Syllabus for 2023, with the aim of enhancing students' conceptual understanding.

JEE Main Scholarship Test Kit (Class 11): Narayana | Physics WallahAakash Unacademy

NEET Scholarship Test Kit (Class 11): Narayana | Physics Wallah Aakash | ALLEN

Class 11 Physics Chapter 9 NCERT solutions are part of NCERT Solutions for Class 11 Physics. If a rubber band is stretched by applying a variable force after a particular amount of force the rubber band breaks. The breakage happens when the applied force is beyond the elastic limit. To compare the elastic limit we use the term modulus of elasticity. The Mechanical Properties Of Solids Class 11 solutions mainly deal with questions related to the concepts of stress, strain, and modulus of elasticity. If these concepts are clear then it is very easy to understand the CBSE NCERT solutions for Class 11 Physics chapter 9 Mechanical Properties Of Solids. The chapter is small in length and easy to score. Class 11 Physics Chapter 9 question answer helps students in their preparations. NCERT is considered the bible for many competitive exams.

**According to the CBSE Syllabus for the academic year 2023-24, the chapter you previously referred to as Chapter 9, " Mechanical properties of solids," has been renumbered as Chapter 8.

## NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Solids

Access NCERT Solutions for Class 11 Physics Chapter 9 Mechanical Properties of Solids Exercise

Let the Young's Modulus of steel and copper be Y S and Y C respectively.

Length of the steel wire l S = 4.7 m

Length of the copper wire l C = 4.7 m

The cross-sectional area of the steel wire A S = $3.0 \times 10^{-5} m^2$

The cross-sectional area of the Copper wire A C = $4.0 \times 10^{-5} m^2$

Let the load and the change in the length be F and $\Delta l$ respectively

$\\Y=\frac{Fl}{A\Delta l}\\ \frac{F}{\Delta l}=\frac{AY}{l}$

Since F and $\Delta l$ is the same for both wires we have

$\\\frac{A_{S}Y_{S}}{l_{S}}=\frac{A_{C}Y_{C}}{l_{C}}\\ \frac{Y_{S}}{Y_{C}}=\frac{A_{C}l_{S}}{A_{S}l_{C}}\\ \frac{Y_{S}}{Y_{C}}=\frac{4.0\times 10^{-5}\times 4.7}{3.0\times 10^{-5}\times3.5}\\ \frac{Y_{S}}{Y_{C}}=1.79$

The ratio of Young’s modulus of steel to that of copper is 1.79.

Young’s modulus is given as the ratio of stress to strain when the body is behaving elastically.

For the given material

$\\Y=\frac{Stress}{Strain}\\ Y=\frac{150\times 10^{6}}{0.002}\\ Y=7.5\times 10^{2}Nm^{-2}$

The Yield Strength is approximately $3\times 10^{8}Nm^{-2}$ for the given material. We can see above this value of strain, the body stops behaving elastically.

As we can see in the given Stress-Strain graphs that the slope is more in the graph corresponding to material A. We conclude that A has a greater Young's Modulus.

The material which fractures at higher stress is said to be stronger. As we can see in the given Stress-Strain graphs the stress at which the material fractures is higher in A than that in B we conclude that A is the stronger material.

False: Young's Modulus is defined as the ratio of the stress applied on a material and the corresponding strain that occurs. As for the same amount of pressure applied on a piece of rubber and steel, the elongation will be much lesser in case of steel than that in the case of rubber and therefore the Young's Modulus of rubber is lesser than that of steel.

True: As the force acts Normal to the parallel planes in which helical parts of the wire lie, the actual length of the wire would not change but it's shape would. Therefore the amount of elongation of the coil taking place for corresponding stress depends upon the Shear Modulus of elasticity.

Tension in the steel wire is F 1

$\\F_{1}=(4+6)\times 9.8\\ F_{1}=98N$

Length of steel wire l 1 = 1.5 m

The diameter of the steel wire, d = 0.25 cm

$\\A=\pi \left ( \frac{d}{2} \right )^{2}\\ A=\pi \times \left ( \frac{0.25\times 10^{-2}}{2} \right )^{2}\\ A=4.9\times 10^{-6}m^{2}$

Area od the steel wire, $A=4.9\times 10^{-6}\ m^{2}$

Let the elongation in the steel wire be $\Delta l_{1}$

Young's Modulus of steel, Y 1 = $2\times 10^{11}Nm^{-2}$

$\\Y_{1}=\frac{F_{1}l_{1}}{\Delta l_{1}A }\\ \Delta l_{1}=\frac{F_{1}l_{1}}{Y_{1}A}\\ \Delta l_{1}=\frac{98\times 1.5}{2\times 10^{11}\times 4.9\times 10^{-6}}\\ \Delta l_{1}=1.5\times 10^{-4}\ m$

Tension in the Brass wire is F 2

$\\F_{2}=(6)\times 9.8\\ F_{2}=58.8N$

Length of Brass wire l 2 = 1.5 m

Area od the brass wire, $A=4.9\times 10^{-6}\ m^{2}$

Let the elongation in the steel wire be $\Delta l_{2}$

Young's Modulus of steel, Y 2 = $0.91\times 10^{11}Nm^{-2}$

$\\ \Delta l_{2}=\frac{F_{2}l_{2}}{Y_{2}A}\\ \Delta l_{2}=\frac{58.8\times 1}{0.91\times 10^{11}\times 4.9\times 10^{-6}}\\ \Delta l_{2}=1.32\times 10^{-4}\ m$

Edge of the aluminium cube, l = 10 cm = 0.1 m

Area of a face of the Aluminium cube, A = l 2 = 0.01 m 2

Tangential Force is F

$\\F=100\times 9.8\\ F=980\ N$

Tangential Stress is F/A

$\\\frac{F}{A}=\frac{980}{0.01}\\ \frac{F}{A}=98000N$

Shear modulus of aluminium $\eta =2.5\times 10^{10}Nm^{-2}$

$\\Tangential\ Strain=\frac{\frac{F}{A}}{\eta }\\ =\frac{98000}{2.5\times 10^{10}}\\ =3.92\times 10^{-6}$

Let the Vertical deflection be $\Delta l$

$\\\Delta l=Tangential\ Stress\times Side \\\Delta l=3.92\times 10^{-6}\times 0.1\\ \Delta l=3.92\times 10^{-7}m$

Inner radii of each column, r 1 = 30 cm = 0.3 m

Outer radii of each colum, r 2 = 60 cm = 0.6 m

Mass of the structure, m = 50000 kg

Stress on each column is P

$\\P=\frac{50000\times 9.8}{4\times \pi \times (0.6^{2}-0.3^{2})}\\ P=1.444\times 10^{5}Nm^{-2}$

Youngs Modulus of steel is $Y=2\times 10^{11}Nm^{-2}$

$\\Compressional\ strain=\frac{P}{Y} \\=\frac{1.444\times 10^{5}}{2\times 10^{11}}\\ =7.22\times 10^{-7}$

Length of the copper piece, l = 19.1 mm

The breadth of the copper piece, b = 15.2 mm

Force acting, F = 44500 N

Modulus of Elasticity of copper, $\eta =42\times 10^{9}Nm^{-2}$

$\\Strain=\frac{F}{A\eta }\\ =\frac{F}{lb\eta }\\ =\frac{44500}{15.2\times 10^{-3}\times 19.1\times 10^{-3}\times 42\times 10^{9}}\\ =3.65\times 10^{-3}$

Let the maximum Load the Cable Can support be T

Maximum Stress Allowed, P = 10 8 N m -2

Radius of Cable, r = 1.5 cm

$\\T=P\pi r^{2}\\ T=10^{8}\times \pi \times (1.5\times 10^{-2})^{2}\\ T=7.068\times 10^{4}N$

Each wire must support the same load and are of the same length and therefore should undergo the same extension. This, in turn, means they should undergo the same strain.

$\\Y=\frac{Fl}{\Delta lA}\\ Y=\frac{4Fl}{\Delta l\pi d^{2}}\\ Yd^{2}=k$ As F, l and $\Delta l$ are equal for all wires

$Y_{iron}=1.9\times 10^{11}Nm^{-2}$

$Y_{copper}=1.1\times 10^{11}Nm^{-2}$

$\\\frac{d_{iron}}{d_{copper}}=\sqrt{\frac{Y_{copper}}{Y_{iron}}}\\ \frac{d_{iron}}{d_{copper}}=\sqrt{\frac{1.1\times 10^{11}}{1.9\times 10^{11}}}\\ \frac{d_{iron}}{d_{copper}}=0.761$

Mass of the body = 14.5 kg

Angular velocity, $\omega$ = 2 rev/s

$\omega =4\pi \ rad/s$

The radius of the circle, r = 1.0 m

Tension in the wire when the body is at the lowest point is T

$\\T=mg+m\omega ^{2}r\\ T=14.5\times 9.8+14.5\times (4\pi )^{2}\\ T=2431.84N$

Cross-Sectional Area of wire, A = 0.065 cm 2

Young's Modulus of steel, $Y=2\times 10^{11}Nm^{-2}$

$\\\Delta l=\frac{Fl}{AY}\\ \Delta l=\frac{2431.84\times1}{0.065\times 10^{-4}\times 2\times 10^{11}}\\ \Delta l=1.87 mm$

Pressure Increase, P = 100.0 atm

Initial Volume = 100.0 l

Final volume = 100.5 l

Change in Volume = 0.5 l

Let the Bulk Modulus of water be B

$\\B=\frac{Stress}{Volumetric\ Strain}\\ B=\frac{P}{\frac{\Delta V}{V}}\\ B=\frac{100\times 1.013\times 10^{5}\times 100\times 10^{-3}}{0.5\times 10^{-3}}\\ B=2.026\times 10^{9}Nm^{-2}$

The bulk modulus of air is $B_{a}=1.0\times 10^{5}Nm^{-2}$

The Ratio of the Bulk Modulus of water to that of air is

$\\\frac{B}{B_{a}}=\frac{2.026\times 10^{9}}{1.0\times 10^{5}}\\ \frac{B}{B_{a}}=20260$

This ratio is large as for the same pressure difference the strain will be much larger in the air than that in water.

Water at the surface is under 1 atm pressure.

At the depth, the pressure is 80 atm.

Change in pressure is $\Delta P=79\ atm$

Bulk Modulus of water is $B=2.2\times 10^{9}Nm^{-2}$

$\\B=-\frac{P}{\frac{\Delta V}{V}}\\ \frac{\Delta V}{V}=-\frac{P}{B} \\\frac{\Delta V}{V}=-\frac{79\times 1.013\times 10^{5}}{2.2\times 10^{9}}\\ \frac{\Delta V}{V}=-3.638\times 10^{-3}$

The negative sign signifies that for the same given mass the Volume has decreased

The density of water at the surface $\rho=1.03\times 10^{3}\ kg\ m^{-3}$

Let the density at the given depth be $\rho '$

Let a certain mass occupy V volume at the surface

$\\\rho=\frac{m}{V}\\$

$\\\rho'=\frac{m}{V+\Delta V}\\$

Dividing the numerator and denominator of RHS by V we get

$\\\rho'=\frac{\frac{m}{V}}{1+\frac{\Delta V}{V}}\\ \rho'=\frac{\rho }{1+\frac{\Delta V}{V}}\\ \rho'=\frac{1.03\times 10^{3}}{1+(-3.638\times 10^{-3})}\\ \rho'=1.034\times 10^{3}\ kg\ m^{-3}$

The density of water at a depth where pressure is 80.0 atm is $1.034\times 10^{3}\ kg\ m^{-3}$ .

Bulk's Modulus of Glass is $B_{G}=3.7\times 10^{10}Nm^{-2}$

Pressure is P = 10 atm.

The fractional change in Volume would be given as

$\\\frac{\Delta V}{V}=\frac{P}{B}\\ \frac{\Delta V}{V}=\frac{10\times 1.013\times 10^{5}}{3.7\times 10^{10}}\\ \frac{\Delta V}{V}=2.737\times 10^{-5}$

The fractional change in Volume is $2.737\times 10^{-5}$

The bulk modulus of copper is $B_{C}=140GPa=1.4\times 10^{11}Nm^{-2}$

Edge of copper cube is s = 10 cm = 0.1 m

Volume Of copper cube is V = s 3

V = (0.1) 3

V = 0.001 m 3

Hydraulic Pressure applies is $P=7.0\times 10^{6}Pa$

From the definition of bulk modulus

$\\B_{C}=\frac{P}{\frac{\Delta V}{V}}\\ \frac{\Delta V}{V}=\frac{P}{B_{C}}\\ \frac{\Delta V}{V}=\frac{7\times 10^{6}}{1.4\times 10^{11}} \frac{\Delta V}{V}=5\times 10^{-5}$

The volumetric strain is $5\times 10^{-5}$

Volume contraction will be

$\\\Delta V=Volumetric\ Strain\times Initial\ Volume\\ \Delta V=5\times 10^{-5}\times 10^{-3}\\ \Delta V=5\times 10^{-8}m^{3}\\ \Delta V=5\times 10^{-2}cm^{3}$

The volume contraction has such a small value even under high pressure because of the extremely large value of bulk modulus of copper.

Change in volume is $\Delta V=0.10 \%$

$\\Volumetric\ Strain =\frac{0.1}{100}\\ \frac{\Delta V}{V}=0.001$

Bulk modulus of water is $B_{w}=2.2\times 10^{9}\ Nm^{-2}$

$\\B_{w}=\frac{P}{\frac{\Delta V}{V}}\\ P=\frac{\Delta V}{V}\times B_{w}\\ P=0.001\times 2.2\times 10^{9}\\ P=2.2\times 10^{6}Pa$

A pressure of $2.2\times 10^{6}Pa$ is to be applied so that a litre of water compresses by 0.1%.

Note: The answer is independent of the volume of water taken into consideration. It only depends upon the percentage change.

The diameter of at the end of the anvil, d = 0.50 mm

Cross-sectional area at the end of the anvil is A

$\\A=\pi \left ( \frac{d}{2} \right )^{2}\\ A=\pi \times \left ( \frac{0.50\times 10^{-3}}{2} \right )^{2}\\ A=1.96\times 10^{-7}m^{2}$

Compressional Force applied, F = 50000N

The pressure at the tip of the anvil is P

$\\P=\frac{F}{A}\\ P=\frac{50000}{1.96\times 10^{-7}}\\ P=2.55\times 10^{11}Nm^{-2}$

The pressure at the tip of the anvil is $2.55\times 10^{11}Nm^{-2}$ .

Cross-Sectional Area of wire A is A A = 1 mm 2

Cross-Sectional Area of wire B is A B = 2 mm 2

Let the Mass m be suspended at x distance From the wire A

Let the Tension in the two wires A and B be F A and F B respectively

Since the Stress in the wires is equal

$\\\frac{F_{A}}{A_{A}}=\frac{F_{B}}{A_{B}}\\ \frac{F_{A}}{1}=\frac{F_{B}}{2}\\ 2F_{A}=F_{B}$

Equating moments of the Tension in the wires about the point where mass m is suspended we have

$\\xF_{A}=(1.05-x)F_{B}\\ xF_{A}=(1.05-x)\times 2F_{A}\\ x=2.1-2x\\ x=0.7m$

The Load should be suspended at a point 70 cm from a wire A such that there are equal stresses in the two wires.

Cross-Sectional Area of wire A is A A = 1 mm 2

Cross-Sectional Area of wire B is A B = 2 mm 2

Let the Mass m be suspended at y distance From the wire A

Let the Tension in the two wires A and B be F A and F B respectively

Since the Strain in the wires is equal

$\\\frac{F_{A}}{A_{A}Y_{S}}=\frac{F_{B}}{A_{B}Y_{Al}}\\ \frac{F_{A}}{F_{B}}=\frac{A_{A}Y_{S}}{A_{B}Y_{Al}}\\ \frac{F_{A}}{F_{B}}=\frac{1\times 2\times 10^{11}}{2\times 7\times 10^{10}}\\ \frac{F_{A}}{F_{B}}=\frac{10}{7}$

Equating moments of the Tension in the wires about the point where mass m is suspended we have

$\\yF_{A}=(1.05-y)F_{B}\\ yF_{A}=(1.05-y)\times \frac{7}{10}F_{A}\\ 10y=7.35-7y\\ y=0.432m$

The Load should be suspended at a point 43.2 cm from the wire A such that there is an equal strain in the two wires.

Let the ends of the steel wire be called A and B.

length of the wire is 2l = 1 m.

The cross-sectional area of the wire is $A=0.50\times 10^{-2}cm^{2}$

Let the depression at the midpoint due to the suspended 100 g be y.

Change in the length of the wire is $\Delta l$

$\\\Delta l=AD+DB-AB\\ \Delta l=\sqrt{l^{2}+y^{2}}+\sqrt{l^{2}+y^{2}}-2l\\ \Delta l=2\sqrt{l^{2}+yx^{2}}-2l\\ \Delta l=2l\left (\left ( 1+\frac{y^{2}}{l^{2}} \right )^{\frac{1}{2}}-1 \right )\\ \Delta l=2l(1+\frac{y^{2}}{2l^{2}}-1)\\ \Delta l=\frac{y^{2}}{l}$

The strain is $\frac{\Delta l}{2l}=\frac{y^{2}}{2l^{2}}$

The vertical components of the tension in the arms balance the weight of the suspended mass, we have

$\\2Fcos\theta =mg\\ 2F\frac{y}{\sqrt{l^{2}+y^{2}}}=mg\\ F=\frac{mg\sqrt{l^{2}+y^{2}}}{2y}\\ F=\frac{mgl}{2y}$

The stress in the wire will be

$\frac{F}{A}=\frac{mgl}{2Ay}$

The Young's Modulus of steel is $Y=2\times 10^{11}Nm^{-2}$

$\\Y=\frac{Stress}{Strain}\\ Y=\frac{\frac{mgl}{2Ay}}{\frac{y^{2}}{2l^{2}}}\\ Y=\frac{mgl^{3}}{Ay^{3}}\\$

$\\y=\left ( \frac{mgl^{3}}{AY} \right )^{\frac{1}{3}}\\ y=\left ( \frac{100\times 10^{-3}\times 9.8\times (0.5)^{3}}{0.5\times 10^{-2}\times 10^{-4}\times 2\times 10^{11}} \right )\\ y=1.074\times 10^{-2}m\\ y=1.074cm$

The depression at the mid-point of the steel wire will be 1.074 cm.

Diameter of each rivet, d = 6.0 mm

Maximum Stress $P=6.9\times 10^{7}Nm^{-2}$

The number of rivets, n = 4.

The maximum tension that can be exerted is T

$\\T=nP\pi \left ( \frac{d}{2} \right )^{2}\\ T=4\times 6.9\times 10^{7}\times \pi \times \left ( \frac{6\times 10^{-3}}{2} \right )^{2}\\ T=7803.71N$

The pressure at the bottom of the trench, $P=1.1\times 10^{8}Pa$

The initial volume of the steel ball, V = 0.32 m 3

Bulk Modulus of steel, $B=1.6\times 10^{11}Nm^{-2}$

$\\B=\frac{P}{\frac{\Delta V}{V}}\\ \Delta V=\frac{PV}{B}\\ \Delta V=\frac{1.1\times 10^{8}\times 0.32}{1.6\times 10^{11}}\\ \Delta V=2.2\times 10^{-4}m^{3}$

The change in the volume of the ball when it reaches the bottom of the trench is $2.2\times 10^{-4}m^{3}$ .

Class 11 Physics Chapter 9 exercise solutions hold significant importance for students. Questions related to the Mechanical Properties of Solids are commonly featured in Class 11 examinations, making it a crucial topic for those aiming to achieve high marks in both school exams and entrance exams. To enhance their understanding of this chapter, students are encouraged to solve the mechanical properties of solids exercise provided at the end of the chapter.

Mechanical properties of solids class 11 exercise explore the fundamental concept of determining a solid's mechanical properties, a central theme in Physics. Students will delve into topics such as Young's modulus for materials like copper and steel. They will learn to extract valuable information, including yield strength, from graph plots and compare stress-strain relation graphs to determine Young's modulus and strength values.

By mastering the content in this class 11 physics ch 9 ncert solutions, students will not only excel in their academic examinations but also gain a deeper insight into the mechanical behaviour of materials, a skill that can be valuable in various real-world applications.

## NCERT Solutions for Class 11 Physics Chapter Wise

 Chapter 1 Physical world Chapter 2 Units and Measurement Chapter 3 Motion in a straight line Chapter 4 Motion in a Plane Chapter 5 Laws of Motion Chapter 6 Work, Energy and Power Chapter 7 System of Particles and Rotational motion Chapter 8 Gravitation Chapter 9 Mechanical Properties of Solids Chapter 10 Mechanical Properties of Fluids Chapter 11 Thermal Properties of Matter Chapter 12 Thermodynamics Chapter 13 Kinetic Theory Chapter 14 Oscillations Chapter 15 Waves

### Mechanical properties of solids numericals: Important Formulas and Diagrams + eBook link

Here are some important formulas and diagrams for mechanical properties of solids class 11 exercise. You can also access the eBook link for comprehensive study materials.

• Hooke's law

• longitudinal strain

JEE Main Highest Scoring Chapters & Topics
Just Study 40% Syllabus and Score upto 100%

The ratio of change in length to the original length.

• A wire of length L and radius r is clamped to a rigid support and a mass m is attached to the other end, then Young's modulus is

L = Original length

= Change in length

• #### Pressure

Pressure applied by a liquid column, p = hρg

• #### Viscous Force

(F)= -η A (dv/dx)

here,

(dv/dx) = rate of change of the velocity with distance and velocity gradient, A = area of cross-section and coefficient of viscosity

• #### Variation in Viscosity

nt= no/(1+αt+βt2)

where no and nt are coefficients of viscosities at 0°C and t°C, α and β are constants

• #### Poiseuille’s Formula

ν= π/2(pr4/ηl)

Where:

p = pressure difference across the two ends of the tube, r = radius of the tube,n = coefficient of viscosity and l = length of the tube

These are some of the important formulas that play a crucial role in understanding the concepts covered in NCERT Solutions class 11 physics chapter 9. Utilize them effectively for your studies and problem-solving.

## Importance of Mechanical Properties Of Solids Class 11 Solutions

By practising NCERT solutions for class 11, you will be able to answer most of the numerical problems asked in final exams for Class 11 and other competitive exams like NEET and JEE mains. The chapter Mechanical Properties of Solids come under the unit properties of bulk matter for NEET and properties of solids and liquids for JEE Mains. Two or three questions are expected for NEET from the unit properties of bulk matter out of which one question is expected from the chapter Mechanical Properties of Solids and in JEE Mains one question may be asked from Mechanical Properties of Solids.

## Key features of mechanical properties of solids exercise solutions

Comprehensive Coverage: NCERT class 11 physics chapter 9 question answer cover all the topics and concepts present in the chapter, ensuring a thorough understanding of mechanical properties of solids.

Step-by-Step Solutions: Detailed step-by-step numericals on mechanical properties of solids class 11 for each question are provided, making it easy for students to follow and grasp the concepts.

Clarity and Simplicity: The mechanical properties of solids numericals are explained in a clear and simple language, making complex concepts easy to understand.

Diagrams and Graphs: Wherever necessary, diagrams and graphs are included to enhance visual understanding and clarify concepts.

Concise Summaries: NCERT mechanical properties of solids exercise solutions often include concise summaries of the main points in each section, helping students revise and retain important information.

Examination-Oriented: The mechanical properties of solids class 11 numericals are designed to help students prepare for exams, including CBSE board exams and various competitive exams.

NCERT Solutions for Class 11 Subject wise

## Subject wise NCERT Exemplar solutions

1. What are the topics covered in the Class 11 chapter Mechanical Properties of Solids

The topics covered in the NCERT book Class 11 physics chapter 9 are

• Elastic behaviour of solids
• Stress and strain
• Hooke’s law
• Stress-strain curve
• Elastic moduli
• Applications of elastic behaviour of materials
2. What is the weightage of the chapter mechanical properties of solids for JEE Main exam

One question may be asked from mechanical properties of solids for JEE Main exam. To practice more questions refer to previous year JEE main papers, NCERT book and NCERT exemplar problems.

3. Can using NCERT Solutions for Class 11 Physics Chapter 9 improve a student's performance and lead to a higher score in CBSE exams?

The chapter 9 physics class 11 ncert solutions are designed to facilitate easy comprehension of the concepts by students. The solutions are prepared by the faculty at careers360, keeping in mind the latest CBSE syllabus and guidelines. The language used in the solutions is simple and clear to enable students to understand the method of solving complex problems effortlessly.

4. is mechanical properties of solids class 11 exercise solutions important chapter for board ?

Yes, the chapter "Mechanical Properties of Solids" in Class 11 is important for board exams as it covers fundamental concepts frequently tested in physics examinations.

## Upcoming School Exams

#### National Institute of Open Schooling 12th Examination

Admit Card Date:28 March,2024 - 22 May,2024

#### National Institute of Open Schooling 10th examination

Admit Card Date:28 March,2024 - 22 May,2024

#### Punjab Board of Secondary Education 12th Examination

Exam Date:05 April,2024 - 27 April,2024

#### Bihar Board 12th Examination

Admit Card Date:19 April,2024 - 11 May,2024

#### Nagaland Board High School Leaving Certificate Examination

Result Date:26 April,2024 - 26 April,2024

Get answers from students and experts

A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

 Option 1) Option 2) Option 3) Option 4)

A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

 Option 1) 2.45×10−3 kg Option 2)  6.45×10−3 kg Option 3)  9.89×10−3 kg Option 4) 12.89×10−3 kg

An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

 Option 1) Option 2) Option 3) Option 4)

A particle is projected at 600   to the horizontal with a kinetic energy . The kinetic energy at the highest point

 Option 1) Option 2) Option 3) Option 4)

In the reaction,

 Option 1)   at STP  is produced for every mole   consumed Option 2)   is consumed for ever      produced Option 3) is produced regardless of temperature and pressure for every mole Al that reacts Option 4) at STP is produced for every mole Al that reacts .

How many moles of magnesium phosphate, will contain 0.25 mole of oxygen atoms?

 Option 1) 0.02 Option 2) 3.125 × 10-2 Option 3) 1.25 × 10-2 Option 4) 2.5 × 10-2

If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

 Option 1) decrease twice Option 2) increase two fold Option 3) remain unchanged Option 4) be a function of the molecular mass of the substance.

With increase of temperature, which of these changes?

 Option 1) Molality Option 2) Weight fraction of solute Option 3) Fraction of solute present in water Option 4) Mole fraction.

Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

 Option 1) twice that in 60 g carbon Option 2) 6.023 × 1022 Option 3) half that in 8 g He Option 4) 558.5 × 6.023 × 1023

A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

 Option 1) less than 3 Option 2) more than 3 but less than 6 Option 3) more than 6 but less than 9 Option 4) more than 9

Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.

4 Jobs Available
##### Bio Medical Engineer

The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary.

4 Jobs Available
##### Ethical Hacker

A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.

3 Jobs Available
##### GIS Expert

GIS officer work on various GIS software to conduct a study and gather spatial and non-spatial information. GIS experts update the GIS data and maintain it. The databases include aerial or satellite imagery, latitudinal and longitudinal coordinates, and manually digitized images of maps. In a career as GIS expert, one is responsible for creating online and mobile maps.

3 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Geothermal Engineer

Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.

3 Jobs Available
##### Database Architect

If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi

3 Jobs Available
##### Remote Sensing Technician

Individuals who opt for a career as a remote sensing technician possess unique personalities. Remote sensing analysts seem to be rational human beings, they are strong, independent, persistent, sincere, realistic and resourceful. Some of them are analytical as well, which means they are intelligent, introspective and inquisitive.

Remote sensing scientists use remote sensing technology to support scientists in fields such as community planning, flight planning or the management of natural resources. Analysing data collected from aircraft, satellites or ground-based platforms using statistical analysis software, image analysis software or Geographic Information Systems (GIS) is a significant part of their work. Do you want to learn how to become remote sensing technician? There's no need to be concerned; we've devised a simple remote sensing technician career path for you. Scroll through the pages and read.

3 Jobs Available
##### Budget Analyst

Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.

4 Jobs Available
##### Data Analyst

The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

3 Jobs Available
##### Underwriter

An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Operations Manager

Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

3 Jobs Available
##### Stock Analyst

Individuals who opt for a career as a stock analyst examine the company's investments makes decisions and keep track of financial securities. The nature of such investments will differ from one business to the next. Individuals in the stock analyst career use data mining to forecast a company's profits and revenues, advise clients on whether to buy or sell, participate in seminars, and discussing financial matters with executives and evaluate annual reports.

2 Jobs Available
##### Researcher

A Researcher is a professional who is responsible for collecting data and information by reviewing the literature and conducting experiments and surveys. He or she uses various methodological processes to provide accurate data and information that is utilised by academicians and other industry professionals. Here, we will discuss what is a researcher, the researcher's salary, types of researchers.

2 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

5 Jobs Available
##### Transportation Planner

A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

3 Jobs Available
##### Environmental Engineer

Individuals who opt for a career as an environmental engineer are construction professionals who utilise the skills and knowledge of biology, soil science, chemistry and the concept of engineering to design and develop projects that serve as solutions to various environmental problems.

2 Jobs Available
##### Safety Manager

A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

2 Jobs Available
##### Conservation Architect

A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.

2 Jobs Available
##### Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.

2 Jobs Available
##### Highway Engineer

Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

2 Jobs Available
##### Field Surveyor

Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials.

2 Jobs Available
##### Orthotist and Prosthetist

Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

6 Jobs Available
##### Pathologist

A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

5 Jobs Available
##### Gynaecologist

Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth.

4 Jobs Available
##### Audiologist

The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

3 Jobs Available
##### Oncologist

An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

3 Jobs Available
##### Anatomist

Are you searching for an ‘Anatomist job description’? An Anatomist is a research professional who applies the laws of biological science to determine the ability of bodies of various living organisms including animals and humans to regenerate the damaged or destroyed organs. If you want to know what does an anatomist do, then read the entire article, where we will answer all your questions.

2 Jobs Available
##### Actor

For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs.

4 Jobs Available
##### Acrobat

Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

3 Jobs Available
##### Video Game Designer

Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

3 Jobs Available

Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

3 Jobs Available
##### Choreographer

The word “choreography" actually comes from Greek words that mean “dance writing." Individuals who opt for a career as a choreographer create and direct original dances, in addition to developing interpretations of existing dances. A Choreographer dances and utilises his or her creativity in other aspects of dance performance. For example, he or she may work with the music director to select music or collaborate with other famous choreographers to enhance such performance elements as lighting, costume and set design.

2 Jobs Available
##### Social Media Manager

A career as social media manager involves implementing the company’s or brand’s marketing plan across all social media channels. Social media managers help in building or improving a brand’s or a company’s website traffic, build brand awareness, create and implement marketing and brand strategy. Social media managers are key to important social communication as well.

2 Jobs Available
##### Photographer

Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

2 Jobs Available
##### Producer

An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story.

They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

2 Jobs Available
##### Copy Writer

In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook.

5 Jobs Available
##### Vlogger

In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion.

Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article.

3 Jobs Available
##### Publisher

For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

3 Jobs Available
##### Journalist

Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

3 Jobs Available
##### Editor

Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

3 Jobs Available
##### Reporter

Individuals who opt for a career as a reporter may often be at work on national holidays and festivities. He or she pitches various story ideas and covers news stories in risky situations. Students can pursue a BMC (Bachelor of Mass Communication), B.M.M. (Bachelor of Mass Media), or MAJMC (MA in Journalism and Mass Communication) to become a reporter. While we sit at home reporters travel to locations to collect information that carries a news value.

2 Jobs Available
##### Corporate Executive

Are you searching for a Corporate Executive job description? A Corporate Executive role comes with administrative duties. He or she provides support to the leadership of the organisation. A Corporate Executive fulfils the business purpose and ensures its financial stability. In this article, we are going to discuss how to become corporate executive.

2 Jobs Available
##### Multimedia Specialist

A multimedia specialist is a media professional who creates, audio, videos, graphic image files, computer animations for multimedia applications. He or she is responsible for planning, producing, and maintaining websites and applications.

2 Jobs Available
##### Welding Engineer

Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues.

5 Jobs Available
##### Quality Controller

A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product.

A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available

A QA Lead is in charge of the QA Team. The role of QA Lead comes with the responsibility of assessing services and products in order to determine that he or she meets the quality standards. He or she develops, implements and manages test plans.

2 Jobs Available
##### Structural Engineer

A Structural Engineer designs buildings, bridges, and other related structures. He or she analyzes the structures and makes sure the structures are strong enough to be used by the people. A career as a Structural Engineer requires working in the construction process. It comes under the civil engineering discipline. A Structure Engineer creates structural models with the help of computer-aided design software.

2 Jobs Available
##### Process Development Engineer

The Process Development Engineers design, implement, manufacture, mine, and other production systems using technical knowledge and expertise in the industry. They use computer modeling software to test technologies and machinery. An individual who is opting career as Process Development Engineer is responsible for developing cost-effective and efficient processes. They also monitor the production process and ensure it functions smoothly and efficiently.

2 Jobs Available
##### AWS Solution Architect

An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party.

4 Jobs Available

An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems.

4 Jobs Available
##### Computer Programmer

Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

3 Jobs Available
##### Product Manager

A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.

3 Jobs Available
##### Information Security Manager

Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack

3 Jobs Available
##### Automation Test Engineer

An Automation Test Engineer job involves executing automated test scripts. He or she identifies the project’s problems and troubleshoots them. The role involves documenting the defect using management tools. He or she works with the application team in order to resolve any issues arising during the testing process.

2 Jobs Available