Question

Consider the situation shown in figure . Initially, the spring is unstretched when the system is released from rest. Assuming no friction in the pulley, Find the maximum elongation of the spring.
Concept of Physics - 1 , HC VERMA , Chapter " Work and Energy"

Answer 1

Let mass of the body be m,

Assume that the highest elongation in the spring  be x .
As given No friction in the pulley , Then for the block , Reduction in the potential energy is equal to potential energy stored in spring .

Now, Potential energy in the spring = 1/2 (kx²)
and change in potential energy = mgx 
Hence on equating these two values.
1/2 (kx²) = mgx
$x = 2mg / k$ .

Hence the maximum elongation in the spring is x = 2mg /k .


Hope it Helps.

Answer 2

see the attachment for the answer