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Q.

A vertical spring carries a 5 kg 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 oscillations in 25 s, with an amplitude of 5 cm. The additional force applied is

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a

80 N

b

80π2N

c

4π2N

d

4N

answer is C.

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Detailed Solution

T=2550=12s ⇒ω=2πT=4πrad/s Spring constant k=mω2=5×(4π)2=80π2N/mForce require( to stretch the spring by 5 cm isF=kx=80π2×0.05N=4π2
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A vertical spring carries a 5 kg 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 oscillations in 25 s, with an amplitude of 5 cm. The additional force applied is