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

Answer

B

Explanation

Period of oscillation of spring
`T= 2pi sqrt((m)/(k))`
`therefore 3= 2pi sqrt((m)/(k))" ""…….."(1)`
Periodic time when 1 kg is added to m and
`5= 2pi sqrt((m+1)/(k))" ""…….."(2)`
Taking ratio of eqn. (2) and (1)
`(5)/(3) = sqrt((m+1)/(m))`
`therefore (25)/(9)= (m+1)/(m)" "` [squaring]
`therefore 25m = 9m+9`
`therefore 16m = 9`
`therefore m= (9)/(16)`.