In figure, the ball A is released from rest, when the spring is at its natural (unstretched) length. For the block B of mass M to leave contact with ground at some stage, the minimum mass of A must be

Options

A. 2M
B. M
C. M/2
D. A function of M and the force constant of the spring

Answer

C

Explanation

Let m be minimum mass of ball.
Let mass A moves downwards by x.
From conservation of energy.
`mgx=1/2kx^(2)`
`x=((2mg)/k)`
For mass M to leave contact with ground
`kx=mg`
`k((2mg)/k)=Mg`
`m=M/2`