A body of mass m dropped from a certain height strikes a light vertical fixed spring of stifness k. the height of its fall before touching the spring the if the maximum compression of the spring the equal to `(3 mg)/k` is

Explanation

The change in potential energy between A and B
`= -mg (h+x)`
The change in K.E. between A and B `=0`
The change in spring potential energy
`=(1//2)kx^(2)`
`rArr -mg(h+x)+0+1/2 kx^(2)=0`
` rArr h+x=(k)/(2mg)x^(2)`
`rArr h=(k)/(2mg)x^(2)-x=((k)/(2mg))((3 mg)/(k))^(2)-(3mg)/(k)=(3 mg)/(2k)`