A cage of mass M hangs from a light spring of force constant `k`. A body of mass m falls from height h inside the cage and stricks to its floor. The amplitude of oscillations of the cage will be-

Options

A. `((2mgh)/(k))^(1//2)`
B. `((k)/(2mgh))^(1//2)`
C. `(mg)/(k)`
D. `((mg)/(k))^(1//2)`

Answer

A

Explanation

`mgh = 1/2(M + m) v^(2) = 1/2 kx^(2)`
`mgh = 1/2 kx^(2) rArr x = [(2mgh)/(k)]^(1//2)`