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. (a) `(M+m)/M`
B. (b) `M/(M+m)^(1/2)`
C. (c ) `((M+m)/M)^1/2`
D. (d) `M/(M+m)`

Answer

C

Explanation

(c ) The net force becomes zero at the mean point.
Therefore, linear momentum must be conserved.
:. Mv_(1)=(M+m)v_(2)`
`Masqrtk/M=(M+m)A_(2)sqrtk/(m+M):. (V=Asqrtk/M)`
`A_(1)sqrtM=A_(2)sqrtM+m :. A_(1)/A_(2)=sqrt(m+M)/M`.