Question

A body of mass 3kg collides elastically with another body at rest and then continues to move in the original direction with one half of its original speed. What is the mass of the target body?

• A. 1 kg
• B. 2.5 kg
• C. 2 kg
• D. 5 kg

Answer 1

The correct option is A 1 kg

Let the initial speed of the colliding body be $u$ and mass of the target body be $m$

Also let the velocity of colliding body after the collision be $v_1$ i.e $v_1=\frac{u}{2}$

Given : $m_1=3kg$ $m_2=m$

$u_1=u$ $u_2=0$ $e=1$

Using $v_1=\frac{(m_1-e{m}_2)u_1+(1+e)m_2{u}_2}{m_1+m_2}$

$v_1=\frac{(3-1\times m)u+(1+1)m\left(0\right)}{3+m}$

$v_1=\frac{u}{2}=\frac{(3-1\times m)u}{3+m}$

$⟹m=1$ kg