An ideal spring with spring constant k is hung from the ceiling and a block of mass M is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in the spring is

Explanation

Block starts from rest and will continue moving down until its velocity again becomes zero for an instant . Hence at the time of maximum elengation block comes to rest for a moment . We can say that for given interval of time , initial and final kinetic energies of the block are zero . .In this case wrok doone by gravity and spring are involved and both the forces are conservative forces . Hence total mechanical energy of the system remains constant . For censervation of mechanical energy we can write the following
Loss in gravitational potential energy = gain in spring potential energy
If x is the height descended by the block then same will be equal to elongation of spring , hence we can write the following :
`mgx = 1/2 Kx^(2)`
`rArr " " x = (2mg)/K`