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

Options

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

Answer

C

Explanation

At mean point `F_("not")=0`, so linear momentum must be conserved.
`Mv_(1)=(M+m)v_(2)`
`MA_(1)sqrt((K)/(M))=(M+m)A_(2)sqrt((K)/(m+M))`
`A_(1)sqrt(M)=A_(2)sqrt(M+m)`
`:." "(A_(1))/(A_(2))=sqrt((m+M)/(M))`
Correct choice : ( c ).