Work, Energy And Power

Question

Wired Faculty App

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution is

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{3}}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

Solution

$\frac{1}{\sqrt{2}}$

Let u₁ and v₁ be the initial and final velocities of ball 1 and u₂ and v₂ be the similar
quantities for ball 2.

Here, u₂ = 0 and v₁ = 0

∴ initial K.E

K_i = $\frac{1}{2} {mu}_{1}^{2} + \frac{1}{2} {mu}_{2}^{2}$

K_i = $\frac{1}{2} {mv}_{1}^{2}$

and final K.E

K_f = $\frac{1}{2} {mv}_{1}^{2} + \frac{1}{2} {mv}_{2}^{2}$

K_f = $\frac{1}{2} {mv}_{2}^{2}$

Loss of KE

ΔK = K_i $-$ K_f

= $\frac{1}{2} m_{1}^{2} - \frac{1}{2} {mv}_{2}^{2}$

According to question

$\frac{1}{2} (\frac{1}{2} {mv}_{1}^{2}) = \frac{1}{2} {mu}_{1}^{2} - \frac{1}{2} {mu}_{2}^{2}$

( since half KE is lost by impact )

$u_{1}^{2} = 2 v_{2}^{2}$

⇒ $v_{2} = \frac{u_{1}}{\sqrt{2}}$

The coefficient of restitution is defined as the ratio of the final velocity to the initial velocity after their collision.

∴ Coefficient of restitution,

e = $|\frac{v_{2} - v_{1}}{u_{1} - u_{2}}|$

= $\frac{v_{2}}{v_{1}}$

e = $\frac{1}{\sqrt{2}}$

Some More Questions From Work, Energy and Power Chapter

How many joules are there in one eV?

What is the relation between kWh and Joule?

Does the body at rest possess energy?

By eating two apples, a person starts pushing the wall of room. If food value of apple is 100 calories per apple, how much work he will do in pushing the wall in one hour?

For Daily Free Study Material Join wiredfaculty

Work, Energy And Power

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution is

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{3}}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$

Some More Questions From Work, Energy and Power Chapter

How many joules are there in one eV?

What is the relation between kWh and Joule?

Does the body at rest possess energy?

By eating two apples, a person starts pushing the wall of room. If food value of apple is 100 calories per apple, how much work he will do in pushing the wall in one hour?

A man is rowing upstream and is at rest w.r.t. shore. Is he doing work w.r.t. shore?

Is frictional force conservative?

What is the work done by gravitational force in taking the mass m with constant velocity through height h?

A mass is tied with a string and whirled in horizontal circle. What is the work done by tension force?

Does the work done by force depend upon the velocity at that instant?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Loaction

For Daily Free Study Material Join wiredfaculty

Work, Energy And Power

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution is 122 13 12 32

Some More Questions From Work, Energy and Power Chapter

How many joules are there in one eV?

What is the relation between kWh and Joule?

Does the body at rest possess energy?

By eating two apples, a person starts pushing the wall of room. If food value of apple is 100 calories per apple, how much work he will do in pushing the wall in one hour?

A man is rowing upstream and is at rest w.r.t. shore. Is he doing work w.r.t. shore?

Is frictional force conservative?

What is the work done by gravitational force in taking the mass m with constant velocity through height h?

A mass is tied with a string and whirled in horizontal circle. What is the work done by tension force?

Does the work done by force depend upon the velocity at that instant?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

A ball impinges directly on a similar ball at rest. The first ball is brought to rest by the impact. If half of the kinetic energy is lost by impact, the value of coefficient of restitution is

$\frac{1}{2 \sqrt{2}}$

$\frac{1}{\sqrt{3}}$

$\frac{1}{\sqrt{2}}$

$\frac{\sqrt{3}}{2}$