Question

A block of mass m is attached with a spring of force constant k. The block is kept on a frictionless plank. The other end of the spring is connected with the plank. Mass of the plank is M and it is also kept on a frictionless surface.

Initially, the system is stationary. A sharp impulse P is applied on the block as shown. The maximum compression in the spring will be

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Initial velocity of M:$v_1=\frac{p}{m}$

At the time of maximum compression, velocity of both is same.

Using, conservation of momentum

(M + m) v = p $\Rightarrow v=\frac{P}{M+m}$

Apply conservation of energy:

$\frac{1}{2}m{v}_1{}^2=\frac{1}{2}(M+m)v^2+\frac{1}{2}k{x}_m{}^2$

Solve to get $x_m=P\sqrt{\frac{M}{k(M+m)m}}$