A mass `M` attached to a horizontal spring executes `SHM` with an amplitude `A_(1)`. When mass `M` passes through its mean position a smaller mass `m` is placed over it and both of them move togther with amplitude `A_(2)`. Ratio of `((A_(1))/(A_(2)))` is:

Options

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

Answer

A

Explanation

By law of coohservation of momentum
`Mv_(1) =(m+ M)v_(2)`
`M(A_(1)omega_(1)) =(m+M) (A_(2)omega_(2))`
`[because omega =sqrt((K)/(M))]`
`implies(A_(1))/(A_(2)) =sqrt((m+M)/(M))`