Question

The system shown in the figure is released from rest. The spring gets elongated if:

• A. $M>m$
• B. $M>2m$
• C. $M>\frac{m}{2}$
• D. any value of $M$

Answer 1

The correct option is D any value of $M$

Net pulling force on the system of ($3$ blocks+spring+string) is $(Mg+mg)-mg=Mg$
Total mass pulled $=M+2m$
Thus, acceleration of system:
$a=\frac{Mg}{M+2m}$ downwards
$\because \frac{M}{M+2m}<1$ always for all values of $m$ and $M$
$a<g$, where $a=$ acceleration of system.

$a<g$ means that some opposing force is acting on block $M$ in upward direction, which is spring force. If this force had not acted, then acceleration of mass $M$ would be $g$ downwards.
$\therefore$ Elongation in spring will develop for any value of mass $M$.