`A` mass `M` is suspended from a spring of negligible mass. The spring is pulled a little then released, so that the mass executes simple harmonic motion of time period `T`. If the mass is increased by `m`, the time period becomes `(5T)/(3)`. Find the ratio of `m//M`.

Options

A. `(9)/(16)`
B. `(25)/(16)`
C. `(4)/(5)`
D. `(5)/(4)`

Answer

A

Explanation

`T=2pi sqrt((M)/(K)) and (5T)/(4)= 2pi sqrt((M+m)/(K))`
`therefore ((5)/(4)T)/(T)= sqrt((M+m)/(M)) therefore (25)/(16)= (M+m)/(M)`
`therefore (25)/(16)-1 =(m)/(M) therefore (m)/(M)=(9)/(16)`