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Do you know what the distance of the moon from Earth is? It sounds interesting, right? This chapter will let you know how things we see around us—like speed, distance, and weight—are measured with accuracy using different tools and measuring kits.
The key concepts include SI units, dimensional analysis, significant figures, measurement errors, and how to check the correctness of equations using dimensions. This chapter builds a strong foundation for solving numerical problems with accuracy and precision.
NCERT Exemplar Class 11 Physics Solutions Chapter 2 gives clear and accurate answers to all the questions related to Units and Measurements. Subject experts make these solutions and explain the standard units used worldwide. This chapter helps you understand different types of units, how to measure physical and abstract quantities, and the possible errors that can occur while measuring.
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You can download the PDF of NCERT Exemplar Chapter 2 Solutions to understand the concepts better and revise easily. NCERT is super helpful for doing well in your final exams and competitive exams, too!
Question:1
The number of significant figures in $0.06900$ is:
$a) 5$
$b) 4$
$c) 2$
$d) 3$
Answer:
The answer is option (b) 4Question:2
The sun of the numbers $436.32, 227.2,$and $0.301$ in appropriate significant figures is:
$a)663.821$
$b)664$
$c)663.8$
$d)663.82$
Answer:
The answer is the option $(c) 663.8$Question:3
The mass and volume of a body are $4.237\; g$ and $2.5\; cm^{3}$ , respectively. The density of the material of the body in correct significant figures is:
a) $1.6048 \; g/cm^{3}$
b) $1.69 \; g/cm^{3}$
c) $1.7 \; g/cm^{3}$
d) $1.695 \; g/cm^{3}$
Answer:
The answer to a multiplication or division is rounded off to the same number of significant figures as possessed by the least precise term used in the calculation. The final result should retain as many significant figures as are there in the original number with the least significant figures. In the given question, density should be reported to two significant figures.Question:4
The mass and volume of a body are $4.237\; g$ and $2.5\; cm^{3}$ , respectively. The density of the material of the body in correct significant figures is:
a) $1.6048 \; g/cm^{3}$
b) $1.69 \; g/cm^{3}$
c) $1.7 \; g/cm^{3}$
d) $1.695 \; g/cm^{3}$
Answer:
The answer is the option $(c) 1.7 \; g\; cm^{-3}$Question:5
The numbers $2.745$ and $2.735$ on rounding off to 3 significant figures will give:
a) $2.75$ and $2.74$
b) $2.74$ and $2.73$
c) $2.75$ and $2.73$
d) $2.74$ and $2.74$
Answer:
The answer is the option $(d) 2.74 \; and\; 2.74$Question:6
The length and breadth of a rectangular sheet are $16.2 \; cm$ and $10.1 \; cm$, respectively. The area of the sheet in appropriate significant figures and error is:
a) $164\pm 3\; cm^{2}$
b) $163.62\pm 2.6\; cm^{2}$
c) $163.6\pm 2.6\; cm^{2}$
d) $163.62\pm 3\; cm^{2}$
Answer:
The answer is the option (i) $164\pm 3\; cm^{2}$Question:7
Which of the following pairs of physical quantities does not have same dimensional formula?
a) work and torque
b) angular momentum and Planck’s constant
c) tension and surface tension
d) impulse and linear momentum
Answer:
The answer is option (c): Tension & surface tensionQuestion:8
Measure of two quantities along with the precision of respective measuring instrument is
$A=2.5\; m/s\pm 0.5\; m/s$
$B= 0.10\; s\; \pm 0.01\;s$
The value of AB will be
$a) (0.25 \pm 0.08) \; m$
$b) (0.25 \pm 0.5) m$
$c) (0.25 \pm 0.05) m$
$d) (0.25 \pm 0.135) m$
Answer:
The answer is the option (a) $(0.25\pm 0.08)m$Question:9
You measure two quantities as $A = 1.0 \; m \pm 0.2 \; m, B = 2.0 \; m \pm 0.2 \; m$. We should report correct value for √ AB as:
a) $1.4 \; m \pm 0.4 \; m$
b) $1.41 \; m \pm 0.15\; m$
c) $1.4 \; m \pm 0.3 \; m$
d) $1.4 \; m \pm 0.2\; m$
Answer:
The answer is the option (d) $1.4\pm 0.2\; m$Question:10
Which of the following measurements is most precise?
a)$5.00 mm$
b) $5.00 cm$
c) $5.00 m$
d) $5.00 km$
Answer:
The answer is option (a), $5.00 mm$Question:11
The mean length of an object is $5\; cm$. Which of the following measurements is most accurate?
a) $4.9\; cm$
b) $4.805\; cm$
c) $5.25\; cm$
d) $5.4\; cm$
Answer:
The answer is option (a), $4.9 cm$Question:12
Young’s modulus of steel is $1.9 \times 10^{11} N/m^{2}$. When expressed in CGS units of dynes/cm2, it will be equal to:
a) $1.9 \times 10^{10}$
b) $1.9 \times 10^{11}$
c) $1.9 \times 10^{12}$
d) $1.9 \times 10^{13}$
Answer:
The answer is option (c) $1.9\times 10^{12}$Question:13
If momentum (P), area (A), and time (T) are taken to be fundamental quantities, then energy has the dimensional formula
a)$(P^{1}A^{-1}T^{1})$
b) $(P^{2}A^{1}T^{1})$
c) $(P^{1}A^{-1/2}T^{1})$
d) $(P^{1}A^{1/2}T^{-1})$
Answer:
The answer is the option d) $(P^{1}A^{1/2}T^{-1})$Question:14
On the basis of dimensions, decide which of the following relations for the displacement of a particle undergoing simple harmonic motion is not correct:
a) $y=a\; \sin \; \frac{2\pi t}{T}$
b) $y=a\; \sin \; vt$
c) $y=\frac{a}{T}\sin (\frac{t}{a})$
d) $y=a\sqrt{2}[\sin (\frac{2\pi t}{t})-\cos (\frac{2\pi t}{T})]$
Answer:
The answer is the option (b) $y=a\; \sin \; vt$ and (c) $y=\frac{a}{T}\sin (\frac{t}{a})$Question:15
If P, Q, R are physical quantities, having different dimensions, which of the following combinations can never be a meaningful quantity?
$a) \frac{(P - Q)}{R}$
$b) PQ - R$
$c)\frac{ PQ}{R}$
$d)\frac{ (PR-Q^{2})}{R}$
$e) \frac{(R + Q)}{P}$
Answer:
The answer is the option $a) \frac{(P - Q)}{R}$ and $e) \frac{(R + Q)}{P}$Question:16
Photon is quantum of radiation with energy E = hv where v is frequency and h is Planck’s constant. The dimensions of h are the same as that of:
a) linear impulse
b) angular impulse
c) linear momentum
d) angular momentum
Answer:
The answer is the option (b) Angular Impulse and (d) Angular momentum$= [ML^{2}T^{-1}]$
Thus, the dimensional formulae of Planck’s constant, Angular Impulse and Angular Momentum are the same.
Question:17
If Planck’s constant (h) and speed of light in vacuum (c) are taken as two fundamental quantities, which of the following can in addition be taken to express length, mass, and time in terms of the three chosen fundamental quantities?
a) mass of electron (me)
b) universal gravitational constant (G)
c) charge of electron (e)
d) mass of proton (mp)
Answer:
The answer is the option (a) Mass of electron (me) and (b) Universal gravitational constant (G) and (d) Mass of proton (mp)Question:18
Which of the following ratios express pressure?
a) Force/area
b) Energy/volume
c) Energy/area
d) Force/volume
Answer:
The answer is the option (a) Force/Area and (d) Force/VolumeQuestion:19
Which of the following is not a unit of time?
a) second
b) parsec
c) year
d) light year
Answer:
The answer is the option (b) Parsec and (d) Light yearQuestion:19
Why do we have different units for the same physical quantity?
Answer:
(i) Different orders of quantity are measured by the same physical quantities.Question:20
The radius of atom is of the order of $1A^{\circ}$ and radius of nucleus is of the order of fermi. How many magnitudes higher is the volume of atom as compared to the volume of nucleus?
Answer:
Radius of atom $=1A^{\circ}=10^{-10} \mathrm{~m}$
Radius of nucleus $=1$ fermi $=10^{-15} \mathrm{~m}$
Volume of atom $=\mathrm{V}_{\mathrm{A}}=\frac{4}{3} \pi R_A^3$
Volume of atom $=\frac{4}{3} \pi R_A^3$
Volume of nucleus $\mathrm{V}_{\mathrm{N}}=\frac{4}{3} \pi R_N^3$
$
\frac{V_A}{V_N}=\frac{\frac{4}{3} \pi R_A^3}{\frac{4}{3} \pi R_N^3}
$
$\begin{aligned} & =\left(\frac{R_A}{R_N}\right)^3 \\ & =\left(\frac{10^{-10}}{10^{-15}}\right)^3 \\ & =10^{15}\end{aligned}$
Question:21
Name the device used for measuring the mass of atoms and molecules.
Answer:
The mass spectrograph is the device used for measuring the mass of atoms and molecules.Question:22
Express unified atomic mass unit in kg.
Answer:
We know that the unified atomic mass unit or amu or $u= \frac{1}{12}$ the mass of one $c^{12}$ atomQuestion:23
Answer:
(i) $\theta$ is a dimensionless physical quantity since it is represented by an angle viz. equal to arc/radius.Question:24
Why length, mass and time are chosen as base quantities in mechanics?
Answer:
Length, mass & time is chosen as base quantities in mechanics because unlike other physical quantities, they cannot be derived from any other physical quantities.Question:25
(a) The earth-moon distance is about 60 earth radius. What will be the diameter of the earth (approximately in degrees) as seen from the moon?
(b) Moon is seen to be of $\left ( \frac{1}{2} \right )^{o}$ diameter from the earth. What must be the relative size compared to the Earth?
(c) From parallax measurement, the sun is found to be at a distance of about 400 times the earth-moon distance. Estimate the ratio of the sun's to Earth's diameters.
Answer:
(a) Here we know that, $\theta =$ arc/radiusQuestion:26
Which of the following time-measuring devices is most precise?
(a) A wall clock.
(b) A stopwatch.
(c) A digital watch.
(d) An atomic clock.
Give a reason for your answer.
Answer:
The least counts of the devices are as follows-Question:27
Answer:
It is given that the distance travelled by light from the galaxy to earth = $10^{25}m.$Question:28
Answer:
Let ‘n’ be the no. of the parts on the Vernier scale, n = 50Question:29
Answer:
Thus, $\Omega _{s}= \Omega _{m}$Question:30
Answer:
The dimensions of -Question:31
Give an example of
(a) a physical quantity which has a unit but no dimensions.
(b) a physical quantity which has neither unit nor dimensions.
(c) a constant which has a unit.
(d) a constant which has no unit.
Answer:
(a) A plane angle is an example of a physical quantity which has unit but no dimension since, plane angle = arc/radius in radian & solid angle.Question:32
Answer:
Given :radius = 31 cmQuestion:33
Answer:
We know that,Question:34
Answer:
According to the principle of homogeneity, the dimensional formula on L.H.S. & R.H.S. is equal.Question:35
Answer:
Given data :Question:36
Answer:
Joules is a unit of work/energy, so let us first write the dimensions of energy-Question:37
Answer:
Let us write dimensions of -Question:38
Answer:
As per the information given in the question, the percentage error in $a = (\frac{\Delta a}{a})(100) = 1\; ^{o}/_{o}$Question:39
Answer:
The dimensional formula of –Question:40
Answer:
Let us first write down the dimensions of-Question:41
Answer:
According to Kepler’s 3rd law of planetary motion,Question:42
In an experiment to estimate the size of a molecule of oleic acid, 1mL of oleic acid is dissolved in 19mL of alcohol. Then 1mL of this solution is diluted to 20mL by adding alcohol. Now, 1 drop of this diluted solution is placed on water in a shallow trough. The solution spreads over the surface of water forming one molecule thick layer. Now, lycopodium powder is sprinkled evenly over the film we can calculate the thickness of the film, which will give us the size of the oleic acid molecule.
Read the passage carefully and answer the following questions:
a) Why do we dissolve oleic acid in alcohol?
b) What is the role of lycopodium powder?
c) What would be the volume of oleic acid in each mL of solution prepared?
d) How will you calculate the volume of n drops of this solution of oleic?
e) What will be the volume of oleic acid in one drop of this solution?
Answer:
(a) We can reduce the concentration of oleic acid by dissolving it in a proper solvent to get a molecular level. It can be dissolved in organic solvent alcohol and not ionic solvent water since it is an organic compound.Question:43
a) How many astronomical units (AU) make 1 parsec?
b) Consider the sun like a star at a distance of 2 parsec. When it is seen through a telescope with 100 magnification, what should be the angular size of the star? Sun appears to be (1/2) degree from the earth. Due to atmospheric fluctuations, eye cannot resolve objects smaller than 1 arc minute.
c) Mars has approximately half of the earth’s diameter. When it is closer to the earth it is at about ½ AU from the earth. Calculate at what size it will disappear when seen through the same telescope.
Answer:
(a)1 A.U. long arc subtends the angle of 1s or 1 arc sec at distance of 1 parsec.Question:44
Einstein’s mass-energy relation emerging out of his famous theory of relativity relates mass (m) to energy (E) as E = mc2, where c is speed of light in vacuum. At the nuclear level, the magnitudes of energy are very small. The energy at nuclear level is usually measured in MeV where $1 MeV = 1.6 \times 10^{-13}J$, the masses are measured in unified equivalent of 1u is 931.5 MeV.
a) Show that the energy equivalent of 1 u is 931.5 MeV.
b) A student writes the relation as $1 u = 931.5 MeV$. The teacher points out that the relation is dimensionally incorrect. Write the correct relation.
Answer:
(a) Given :Main Subtopics in NCERT Exemplar Class 11 Physics Solutions Chapter 2 Units and Measurement
This chapter helps students understand how measurement methods have changed over time and teaches them about basic units. With the help of NCERT Exemplar Class 11 Physics Chapter 2 Solutions, students can connect these concepts to real-life measuring tools. It also shows how to use accurate measurements to solve practical problems—like finding the mass of rain clouds, speed of an aircraft using dimensional analysis, or even calculating the distance between stars.
NCERT Exemplar Class 11 Physics Chapter 2 Solutions help students learn about different units used around the world and the standard unit system accepted internationally. The chapter explains how to measure physical quantities like length and mass, as well as abstract ones like time.
You'll also learn about dimensional formulas and equations, which are super useful in solving real-life problems using dimensional analysis. The chapter also explains why significant figures matter in measurements.
It teaches you the difference between accuracy and precision and how to deal with errors in measurements. You'll also get to know the types of errors that can occur in instruments and how to spot and fix them easily.
Chapter 1 | Units and Measurement |
Chapter 2 | Motion in a straight line |
Chapter 3 | Motion in a Plane |
Chapter 4 | Laws of Motion |
Chapter 5 | Work, Energy and Power |
Chapter 6 | System of Particles and Rotational motion |
Chapter 7 | Gravitation |
Chapter 8 | Mechanical Properties of Solids |
Chapter 9 | Mechanical Properties of Fluids |
Chapter 10 | Thermal Properties of Matter |
Chapter 11 | Thermodynamics |
Chapter 12 | Kinetic Theory |
Chapter 13 | Oscillations |
Chapter 14 | Waves |
These solutions from Chapter 2 can help better understand the basic concepts and prepare for your academic exams. Questions of multiple choice type, short answer and long answer types are solved.
These Class 11 physics NCERT exemplar solutions chapter 1 can be downloaded from the website and the solution page directly in PDF format.
This chapter's essential topics are the International System of Units, Measurement of quantities, accuracy and precision, dimensional formulae, and dimensional analysis.
Significant figures show how accurate your measurement is. They help you write your answers correctly and avoid silly mistakes in calculations
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