A body of mass `m` is atteched to the lower end of a spring whose upper end is fixed .The spring has negaligible mass .When the mass `m` is slightly puylled down and released it oscillation with a time period of `3 s` when the mass `m` is increased by `1kg` time period of oscillations becomes `5s` The value of `m` in `kg` is

Options

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

Answer

B

Explanation

`T = 2pi sqrt((m)/(k))`
`3 = 2 pi sqrt((m)/(k))` ….(i)
`5 = 2 pi sqrt((m+1)/(k))`….(ii)
`((1)^(2))/((2)^(2)) rArr (9)/(19) = (m)/(m + 1) rArr m = (9)/(16)`