Question

a body of mass 1 kg makes an elastic collision with another body at rest and continues to move in the original direction after collision with a velocity equal to one by fifth of its original velocity find the mass of the second body ​

Answer 1

Let,

Mass of first body, m_1 = 1 kg

Since the second body was at rest, initial velocity, u_2 = 0.

Given, v_1 = u_1 / 5.

We have to find m_2, mass of second body.

Since the collision is elastic, the momentum and kinetic energy are conserved. These imply,

u_1 + v_1 = u_2 + v_2

6u_1 / 5 = v_2

[because v_1 = u_1 / 5 and u_2 = 0.]

Now, according to Law of Conservation of Linear Momentum,

m_1 u_1 + m_2 u_2 = m_1 v_1 + m_2 v_2

Since u_2 = 0,

m_2 = [m_1 (u_1 - v_1)] / v_2

m_2 = 5[m_1 (u_1 - v_1)] / 6u_1

[because 6u_1 / 5 = v_2]

Since m_1 = 1 kg and v_1 = u_1 / 5,

m_2 = 5 [4u_1 / 5] / 6u_1

m_2 = 4u_1 / 6u_1

m_2 = 2/3 kg