Q 11-05-144JEE MainJEE Main 2021 (18 Mar, Shift 2)Medium
An object of mass $m_1$ collides with another object of mass $m_2$, which is at rest. After the collision the objects move with equal speeds in opposite direction. The ratio of the masses $m_2 : m_1$ is:
Answer: (A) 3 : 1
Treat the collision as elastic. Let $m_1$ move with $u$ before, and let the final velocities be $-v$ and $+v$.
Momentum: $m_1u = (m_2 - m_1)v$. Energy: $m_1u^2 = (m_1 + m_2)v^2$.
Substituting $u = \dfrac{(m_2 - m_1)v}{m_1}$:
$$(m_2 - m_1)^2 = m_1(m_1 + m_2) \Rightarrow m_2^2 = 3m_1m_2 \Rightarrow m_2 = 3m_1$$
So $m_2 : m_1 = 3 : 1$.
Solution by Sreeraj P, M.Sc Physics