Question

In the figure block $A$ is released from rest when the spring is in its natural length. For the block $B$ of mass m to leave contact with the ground at some stage what should be the minimum mass of block $A$?

Answer 1

m:Mass of block A

M:Mass of block B

When B leaves contact its entire weight must be balanced by the spring force(so that the normal reaction goes to zero).

$Kx=Mg$

Where x is the amount by which spring expands.

This would mean the block A has moved down by a amount x.

Using conversation of energy,

$mgx=0.5K{x}^2$

$m=\frac{M}{2}$