`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)), implies T '=2pisqrt((M+n)/(K))`
because T '=`(5)/(3)T implies 2pisqrt((M+m)/(K))=(5)/(3)2pisqrt((M)/(K))`
`implies (M+m)/(K)=(25)/(9)xx(M)/(K)` `implies (m)/(M)=(16)/(9)`