A mass 'M' is suspended from a spring of negligible mass. The spring is pulled a little and then released. It execuutes S.H. oscillations of period T. When mass is increased by 'm', the period becomes `(5)/(4)` T, the ratio `(m)/(M)` is :

Options

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

Answer

A

Explanation

`T=2pi sqrt((M)/(k))" "…(i)`
and `(5T)/(4)=2pi sqrt((M+m)/(k))" "…(ii)`
Dividing (ii) by (i)
`:." "(5)/(4)=sqrt((M+m)/(M))" "implies" "(25)/(16)=(M+m)/(M)`
`:." "(m)/(M)=(9)/(16)`
Hence correct choice is (a).