Question

Two blocks $A$ and $B$ having the same mass collide elastically with each other. the velocity of block $A$ before the collision is $10\text{m/s}$. If block $A$ comes to rest after collision, then what was the velocity of block $B$ before the collision?

• A. $10\text{m/s}$
• B. $0\text{m/s}$
• C. $20\text{m/s}$
• D. $30\text{m/s}$

Answer 1

The correct option is B $0\text{m/s}$

Let the velocity of block B before and after collision be $u_B$ and $v_B$ respectively.
Using conservation of momentum:
$m\times 10+m\times u_B=m\times 0+m\times v_B$
$\Rightarrow v_B=u_B+10\dots \left(i\right)$
and using conservation of energy:
$\frac{1}{2}\times m\times {10}^2+\frac{1}{2}\times m\times u_B^2=\frac{1}{2}\times m\times v_B^2$
$\Rightarrow v_B^2=u_B^2+100\dots \left(ii\right)$

Using $\left(i\right)$ in $\left(ii\right)$:
$u_B^2+20u_B+100=u_B^2+100$
$\Rightarrow 20u_B=0$
$\Rightarrow u_B=0$

So, initially block $B$ was at rest.