Question

A ball $B$ of mass $m$ is projected with some velocity from a block A of mass $2m$ kept on a smooth horizontal surface. The ball strikes the wall elastically and comes back to the block A. Find the distance of block A from the wall when ball reaches back to it. Velocity in $B$ is generated by a compressed spring fixed to block A. When the ball leaves spring, the distance of block from wall is $d$. (Neglect gravity)

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

Answer 1

Answer: (D)

$3d$

Let velocity of ball be $v_1$ and velocity of block be $v_2$

Applying the conservation of momentum for the bigger block and ball
$m{v}_1=2m{v}_2$

$v_2=\frac{v_1}{2}$

Let the block travel a distance $x$ in time $t$

$t=\frac{x}{v_1/2}=\frac{2d+x}{v_1}$

$\Rightarrow 2x=2d+x$
$x=2d$

$\therefore$ Final distance of block A from the wall $=d+x=3d$