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_(1))/(T_(2)) = sqrt((m+1)/(m)) rArr ((3)/(5))^(2) = (m)/(m+1)`
By solving `m = (9)/(16)` kg