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. `25 : 9`
D. `19 : 9`

Answer

A

Explanation

`T_(1)=T,T_(2)=(5)/(4)T`
`(T_(2))/(T_(1))=sqrt((M_(2))/(M_(1)))=sqrt((M+m)/(M))`
`(5T)/(4T)=sqrt((M+m)/(M))`
`(25)/(16)=1+(m)/(M)`
`(25-16)/(16)=(m)/(M)`
`(9)/(16)=(m)/(M)`