Question

The system shown in figure below is released from rest. Initially, the spring is at its natural length. The spring gets elongated after it is released

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

Answer 1

The correct option is D for any value of $M$

Net pulling force on the system is $Mg+mg-mg$ (as spring force is internal and will cancel out) or simply $Mg$. Total mass being pulled is $M+2m$. Hence, acceleration of the system is
$a=\frac{Mg}{M+2m}$
Now since $a<g$, there should be an upward force on $M$ so that its acceleration become less than $g$. It means there is some tension developed in the string. Hence, for any value of $M$ spring will be elongated.