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. `(3)/(4)`
B. `(4)/(3)`
C. `(16)/(9)`
D. `(9)/(16)`

Answer

D

Explanation

`3=2pisqrt((m)/(k))`
`5=2pisqrt((m+1)/(k))`
`(3)/(5)=sqrt((m)/(m+1))`
`(9)/(25)=(m)/(m+1)`
`9m+9=25m`
`16m=9`
`m=(9)/(16)`