A horizontal spring is connedted to a mass `M`. It exectues simple harmonic motion. When the mass `M` passes through its mean position, an object of mass `m` is put on it and they moves together. The ratio of frequencies before and after will be-

Options

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

Answer

A

Explanation

`f = (1)/(m) sqrt((k)/(m)) rArr (f_(1))/(f_(2)) = sqrt((m_(2))/(m_(1)))`
`rArr (f_(1))/(f_(2)) = ((M + m)/(M))^(1//2) = (1 + (m)/(M))^(1//2)`