Motion in a plane

# Motion in a plane

Edited By Team Careers360 | Updated on May 06, 2022 09:23 AM IST

Introduction:
The three equations of motion and motion in a straight line would have been covered. We're going to learn about planar motion now. When we talk about motion in a plane, we're talking about motion in two dimensions and motion in two dimensions examples, because a plane is made up of two dimensions. As a result, we'll consider two axes: the X-axis and the Y-axis. We need to understand motion in one dimension in order to derive equations of motion.

Physical quantities such as work, temperature, and distance can be expressed entirely by their magnitude in everyday life. The relationship between these physical values, on the other hand, maybe explained by arithmetic principles. The direction is just as important as the amount for representing physical variables like acceleration, displacement, and force. Let's look into Plane Motion presently.

The term "velocity" refers to a physical vector quantity that has both a magnitude and a direction. Speed refers to the magnitude or scalar absolute value of velocity. The magnitude of the velocity vector is given by – according to the Pythagorean Theorem.

| v | = v = √ ( vx ²+ vy ² )

The rate at which an object's velocity changes with respect to time is known as acceleration. It can be presented numerically or in terms of components as –

ay= ddt(vy(t)) ………..(Eq.1)

ax= ddt(vx(t)) ………..(Eq.2)

List of topics according to NCERT and JEE Main/NEET syllabus:

• Introduction to Motion in a Plane.
• Scalars and Vectors.
• Resolution of Vectors and Vector Addition.
• Addition and Subtraction of Vectors – Graphical Method.
• Relative Velocity in Two Dimensions.
• General plane motion
• Motion in a plane with constant acceleration
• Projectile Motion.
• projectile motion on inclined plane/projectile on the inclined plane.
• Scalar And Vector Products.
• Scalar Product.
• Difference Between Scalar and Vector.
• Addition and Subtraction Of Vectors.
• Triangular Law Of Vector Addition.
• Vector Product Of Two Vectors And Their Properties.
• Vectors and Their General Properties.
• Resolution Of A Vector In A Plane – Rectangular Components.
• Unit Vectors.
• Vector Notation.
• Relative Motion.
• Relative Velocity.
• Uniform Circular Motion.

Importance of motion in a plane class 11:

From this class 11 physics chapter 4 motion in a plane, you can only expect one question from the chapter. This chapter lays the groundwork for the next topic, rotation, which is crucial for JEE. As a result, we recommend that you do not skip this chapter. Circular motion will be discussed several times in Mechanics.

NCERT Exemplar Solutions Subject wise link:

1. What is the definition of plane motion?

Motion in a plane refers to the movement along the x- and y-axes in a two-dimensional plane.

2. What is the difference between one-dimensional and two-dimensional motion?

One-dimensional motion occurs when an object moves in a straight line regardless of its direction. Two-dimensional motion occurs when an item moves in x and y coordinates at a constant velocity.

3. What is the definition of accelerated motion?

Accelerated motion occurs when the velocity of a moving object increases steadily over time.

4. What is oscillatory motion, and how does it differ from other types of motion?

Oscillatory motion is defined as the movement of an object back and forth around its mean location.

5. What is projectile motion, and how does it differ from other types of motion?

When an object is thrown into the air and the only force acting on it is gravity, it is called projectile motion.

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5 g of Na2SO4 was dissolved in x g of H2O. The change in freezing point was found to be 3.820C.  If Na2SO4 is 81.5% ionised, the value of x (K for water=1.860C kg mol−1) is approximately : (molar mass of S=32 g mol−1 and that of Na=23 g mol−1)
Option: 1  15 g
Option: 2  25 g
Option: 3  45 g
Option: 4  65 g

50 mL of 0.2 M ammonia solution is treated with 25 mL of 0.2 M HCl.  If pKb of ammonia solution is 4.75, the pH of the mixture will be :
Option: 1 3.75
Option: 2 4.75
Option: 3 8.25
Option: 4 9.25

$CH_3-CH=CH-CH_3+Br_2\overset{CCl_4}{\rightarrow}A$

What is A?

Option: 1

Option: 2

Option: 3

Option: 4

None

when heated gives a white solid A and two gases B and C. B and C are two important atmospheric gases. What is A, B and C ?

Option: 1

$\mathrm{A}: \mathrm{NaNO}_2 \mathrm{~B}: \mathrm{O}_2 \mathrm{C}: \mathrm{N}_2$

Option: 2

$A: \mathrm{Na}_2 \mathrm{OB}: \mathrm{O}_2 \mathrm{C}: \mathrm{N}_2$

Option: 3

$A: \mathrm{NaNO}_2 \mathrm{~B}: \mathrm{O}_2 \mathrm{C}: \mathrm{Cl}_2$

Option: 4

$\mathrm{A}: \mathrm{Na}_2 \mathrm{OB}: \mathrm{O}_2 \mathrm{C}: \mathrm{Cl}_2$

$C_1+2 C_2+3 C_3+\ldots .n C_n=$

Option: 1

$2^n$

Option: 2

$\text { n. } 2^n$

Option: 3

$\text { n. } 2^{n-1}$

Option: 4

$n \cdot 2^{n+1}$

A capacitor is made of two square plates each of side 'a' making a very small angle between them, as shown in the figure. The capacitance will be close to :
Option: 1

Option: 2

Option: 3

Option: 4

Among the following compounds, the increasing order of their basic strength is
Option: 1  (I) < (II) < (IV) < (III)
Option: 2  (I) < (II) < (III) < (IV)
Option: 3  (II) < (I) < (IV) < (III)
Option: 4  (II) < (I) < (III) < (IV)

An ideal gas undergoes a quasi static, reversible process in which its molar heat capacity C remains constant.  If during  this process the relation of pressure P and volume V is given by PVn=constant,  then n is given by (Here CP and CV are molar specific heat at constant pressure and constant volume, respectively)
Option: 1  $n=\frac{C_{p}}{C_{v}}$

Option: 2  $n=\frac{C-C_{p}}{C-C_{v}}$

Option: 3 $n=\frac{C_{p}-C}{C-C_{v}}$

Option: 4  $n=\frac{C-C_{v}}{C-C_{p}}$

As shown in the figure, a battery of emf is connected to an inductor L and resistance R in series. The switch is closed at t = 0. The total charge that flows from the battery, between t = 0 and t = tc (tc is the time constant of the circuit ) is :

Option: 1
Option: 2

Option: 3

Option: 4

As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point B. The speed  of the particle at B is x m/s. (Take g = 10 m/s2 ) The value of 'x' to the nearest is ___________.
Option: 1 10
Option: 2 20
Option: 3 40
Option: 4 15