A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3s. When the mass m is increased by `1 kg`, the time period of oscillations becomes 5s. The value of m in kg is

Options

A. `9//16`
B. `3//4`
C. `4//3`
D. `16//9`

Answer

A

Explanation

`T=2pisqrt(m/k)=3sec`, `T.=2pisqrt((m+1)/(k))=5` sec
On squaring and dividing `((m)/(m+1))=((3)/(5))^(2)=(9)/(25)`
`25m=9m+9` so `m=(9)/(16)kg`.