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A body of mass m is attached to the lowe...

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

A

`16/9`

B

`9/16`

C

`3/4`

D

`4/3`

Text Solution

Verified by Experts

The correct Answer is:
B
`T = 2pi sqrt(m/k)`
`3 = 2pi sqrt(m/k) " "....(1)`
`5 = 2pi sqrt((m+ 1)/(k)) " "....(2)`
`((1)^2)/((2)^2) implies 9/25 = m/(m + 1) implies m = 9/16`
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