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

Time period of spring - block system,
`T=2pisqrt((m)/(k))`
For given spring, `Tpropsqrt(m)`
`(T_(1))/(T_(2))=sqrt((m_(1))/(m_(2)))`
Here, `T_(1)=3s,m_(1)=m,T_(2)=5s,m_(2)=m+1`
`(3)/(5)=sqrt((m)/(m+1))or,(9)/(25)=(m)/(m+1)`
`25m=9m+9implies16m=9impliesm=(9)/(16)kg`