Question

A block of mass $m$ moving with speed $v$ collides with another block of mass $2m$ at rest. The lighter block comes to rest after collision. What is the value of coefficient of restitution?

• A. $\frac{1}{2}$
• B. $\frac{1}{3}$
• C. $\frac{3}{4}$
• D. $\frac{1}{4}$

Answer 1

The correct option is A $\frac{1}{2}$

Mass of first block $m_1=m$ and its velocity before collision $u_1=v$

Mass of second block $m_B=2m$ and its velocity before collision $u_2=0$

Velocity of first block after collision $v_1=0$

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

Or $0=\frac{(m-2me)v+(1+e)\left(2m\right)\left(0\right)}{m+2m}$

Or $0=\frac{(1-2e)v}{3}$

Or $1-2e=0$

$⟹e=\frac{1}{2}$