`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. `3/5`
B. `25/9`
C. `16/9`
D. `5/3`

Answer

C

Explanation

`T = 2pisqrt((M)/(k))` and `(5T)/(3) = 2pisqrt((M + m)/(k))`
On driving ` = (5T)/(3T) = sqrt((M + m)/(M))`
`rArr (25)/(9) = (M + m)/(M) rArr (m)/(M) = (16)/(9)`