Question

A ball of mass 4 kg moving on a smooth horizontal surface makes an elastic collision with another ball of mass m at rest in the line of motion of first ball, if after collision first ball moves in the same direction with one fourth of its velocity before collision, then mass of second ball is :

• A. 4 kg
• B. 4.4 kg
• C. 2.4 kg
• D. 2 kg

Answer 1

The correct option is C 2.4 kg

Given, $m_1=4kg$ $u_1=u$ (say) $m_2=m$ & $u_2=0$ (at rest)

also, $v_1=u/4$ and collision is elastic

From collision theory,

$v_1=\left(\frac{m_1-m_2}{m_1+m_2}\right)u_1+\left(\frac{2m_2}{m_1+m_2}\right)u_2$

Put values

$\frac{u}{4}=\left(\frac{4-m}{4+m}\right)u+0\Rightarrow 4+m=4(4-m)\Rightarrow m=\frac{12}{5}=2.4kg$ (Ans)