Q. 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.

In This post you will get answer of Q.
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.

Solution:

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{left(m_{1}-m_{2}right)u_{1}}{m_{1}+m_{2}}+frac{2m_{2}u_{2}}{m_{1}+m_{2}} quadldotsleft(iright) $

$ v_{2} =frac{2m_{1}u_{2}}{m_{1}+m_{2}}+frac{left(m_{2}-m_{1}right)u_{2}}{m_{1}+m_{2}}quad ldots left(iiright) $

where $ m_1 $ and $ m_2 $ are the masses of two bodies and $ u_1 $ and $ u_2 $ are the velocities of two bodies before collision.

If $ m_1 = m_2 $ , then

From $ (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

$ v_1 = u_1 $ and $ v_2 = 2u_1 $

Thus, statement $ B $ is wrong.