Question

Block A of mass $2m$ is hanging from a vertical mass-less spring of spring constant ${}^{\prime }{k}^{\prime }$ and is at rest. A block B of mass m strikes the given block of mass $2m$ with velocity ${}^{\prime }{u}^{\prime }$ and sticks to it as shown. The magnitude of the acceleration of blocks just after collision is

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

Answer 1

Answer: (B)

$\frac{g}{3}$

Elongation in the spring will be $x=\frac{2mg}{k}$.............(1)

Finally,

When mass $m$ strick with $2m$, total Downward force $3mg$

balancing forces, $3mg-kx=3ma$ ...........(2)

On putting the value from equation $1$

$a=\frac{g}{3}$