MyQuestionIcon

2

You visited us 2 times! Enjoying our articles? Unlock Full Access!

The 'e' Equation

A ball collid...

Question

A ball collides directly with another ball at rest and is itself brought to rest by the impact. If one fourth of initial kinetic energy is destroyed in the collision, the coefficient of restitution of the collision is

A

No worries! We‘ve got your back. Try BYJU‘S free classes today!

B

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

D

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C

$m_{1} u_{1} = m_{2} v_{2} a n d e = \frac{V_{2} - V_{1}}{u_{1} - u_{2}} = \frac{V_{2}}{u_{1}} \Rightarrow V_{2} = e u_{1} m_{1} u_{1} = m_{2} e u_{1} \Rightarrow m_{1} = e m_{2}$

Loss of kinetic energy.
$= \frac{1}{2} \frac{m_{1} m_{2}}{m_{1} + m_{2}} (u_{1} - 0)^{2} (1 - e^{2}) = \frac{1}{4} \times \frac{1}{2} m_{1} u_{1}^{2}$

$\frac{m_{2}}{m_{1} + m_{2}} (1 - e^{2}) = \frac{1}{4} \frac{m_{2}}{e m_{2} + m_{2}} (1 - e^{2}) = \frac{1}{4} \Rightarrow 1 - e = \frac{1}{4} e = \frac{3}{4}$

Suggest Corrections

thumbs-up

0

Similar questions

Q. A ball of mass m hits directly another ball of mass

M

at rest and is brought to rest by the impact. One third of the kinetic energy of the ball is lost due to collision. The coefficient of restitution is

Q. 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

Q. A ball of mass

m

moving at a speed

v

makes a head-on collision with an identical ball at rest. The kinetic energy of the balls after the collision is three fourths of the original. Find the coefficient of restitution.

1

collides head on with another identical ball

2

, initially at rest. Velocity of ball

2

after collision becomes two times that of ball

1

after collision. The coefficient of restitution between the two balls is :

1

Collides head-on with another identical ball

2

at rest. The velocity of ball

2

after collision becomes two times to that of ball

1

after a collision. The coefficient of restitution between the two balls is

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Realistic Collisions

PHYSICS

Watch in App

explore_more_icon

Explore more

The 'e' Equation

Standard XII Physics

Join BYJU'S Learning Program

CrossIcon