A mass `M` is suspended from a spring of negiliglible mass the spring is pulled a little and then released so that the mass executes simple harmonic oscillation with a time period `T` If the mass is increases by `m` the time period because `((5)/(4)T)`,The ratio of `(m)/(M)` is

Options

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

Answer

A

Explanation

`T = 2pi sqrt((m)/(k)) rArr m prop T^(2) rArr (m_(2))/(m_(1)) = (T_(2)^(2))/(T_(1)^(2))`
` rArr (M +m)/(M) = = (((5)/(4)T)/(T))^(2) rArr (m)/(M) = (9)/(16)`