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A vertical spring carries a 5kg body and...

A vertical spring carries a `5kg` body and is hanging in equilibrium an additional force is applied so that the spring is further stretched. When released from this position. It performs 50 complete oscillation in 25 s, with an amplitude of 5 cm. The additional force applied is

A

80 N

B

`80pi^2N`

C

`4pi^2N`

D

`4N`

Text Solution

Verified by Experts

The correct Answer is:
C
`T=(25)/(50)=(1)/(2)simpliesomega=(2pi)/(T)=4pi(rad)/(s)`
Spring constant `k=momega^2=5xx(4pi)^2=80pi^2(N)/(m)`
Force required to stretch the spring by 5 cm is
`F=kx=80pi^2xx0.05N=4pi^2`
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