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

Options

A. `(5)/(3)`
B. `(3)/(5)`
C. `(25)/(9)`
D. `(16)/(9)`

Answer

D

Explanation

`T prop sqrt(m) rArr (T_(2))/(T_(1)) = sqrt((m_(2))/(m_(1))) rArr (5)/(3) = sqrt((M +m)/(M))`
`rArr (25)/(9) = (M+m)/(M) rArr (m)/(M) = (16)/(9)`