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

Answer

D

Explanation

`C.O.L.M.`
`MV_(max) = (m + M)V_("new") , V_(max) = A_(1)omega_(1)`
`V_("new") = (MV_(max))/((m + M))`
Now, `V_("new") = A_(2).omega_(2)`
`(MA_(1))/((m + M))sqrt((K)/(M)) = A_(2)sqrt((K)/((m + M)))`
`A_(2) = A_(1)sqrt((M)/((m + M))), (A_(1))/(A_(2)) = ((m + M)/(M))^(1//2)`