A mass (M), attached to a horizontal spring, executes S.H.M. whith amplitude `A_(1). When the mass (M) passes throgh its mean position then shaller mass (m) is placed over it and both of them move together with amplitude `A_(2). The ration of.

Options

A. `(M)/(M+m)`
B. `(M+m)/(M)`
C. `((M)/(M+m))^(1//2)`
D. `((M+m)/(M))^(1//2)`

Answer

D

Explanation

By conservation of momentum
`Mv=(m+M)VimpliesV=(M)/(M+m)v`
`A_2omega_2=(M)/(M+m)A_1omega_1`
`A_1/A_2=((M+m)/(M))(omega_2/omega_1)=((M+m)/(M))((M)/(M+m))^(1//2)`
`=((M+m)/(M))^(1/2)`