Discussion Forum

A block with mass M is connected by a massless spring with stiffness constant k to a rigid wall and moves without friction on a horizontal surface. The block oscillates with small amplitude A about an equilibrium position x₀. Consider two cases : (i) when the block is at x₀  and (ii) when the block is at x=x₀ +A . In both the cases, a particle with mass m (<M)  is softly placed on the block after which they stick to each other. Which of the following statement(s) is (are) true about the motion after the mass m is placed on the mass M?

Answer:

Explanation:

Case-1

Case -II

In caes-I

$Mv_{1}=(M+m)v_{2}\Rightarrow v_{2}=(\frac{M}{M+m})v_{1}$

$\sqrt{\frac{k}{M+m}}A_{2}=(\frac{M}{M+m})\sqrt{\frac{k}{M}}A_{1}$

$A_{2}=\sqrt{\frac{k}{M+m}}A_{1}$

In case-2,     $A_{2}=A_{1}$

$T=2\pi \sqrt{\frac{M+m}{k}}$ in both cases.

 Total energy decreases in first case whereas remain same in 2nd case. Instantaneous speed at x₀ decreases in both cases.