Question

Consider the following statements A and B. Identify the correct choice in the given answers:

A. In a one dimensional perfectly elastic collision between two moving bodies of equal masses, the bodies merely exchange their velocities after collision

B. If a lighter body at rest suffers perfectly elastic collision with a very heavy body moving with a certain velocity, then after collision both travel with same velocity

• A. A and B are correct
• B. Both A and B are wrong
• C. A is correct, B is wrong
• D. A is wrong, B is correct

Answer 1

Answer: (C)

A is correct, B is wrong

Answer 2

for A:

Using the laws of conservation of linear momentum and energy the velocities of two bodies after perfectly elastic collision are given by

$v_{1} = \frac{(m_{1} - m_{2})}{m_{1} + m_{2}} + \frac{2m_{2}u_{2}}{m_{1} + m_{2}}$ …….(i)

$v_{2} = \frac{2m_{1}u_{1}}{m_{1} + m_{2}} + \frac{(m_{2} - m_{1})u_{2}}{m_{1} + m_{2}}$ …….(ii)

Where $m_{1}andm_{2}$are the masses of two bodies and $u_{1}andu_{2}$are the velocities of two bodies before collision.

If $m_{1} = m_{2}$then

Form (i) and (ii), we get

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

i.e., in perfectly elastic collision of two moving bodies of equal masses, the bodies merely exchange their velocities after collision. Thus, statement A is correct.

For B.

In Eqs. (i) and (ii)

If $m_{2} < < m_{1}andu_{2} = 0$then

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

Thus statement B is wrong.