Question

# The length of simple pendulum is 1 m and mass of its bob is 50 g. The bob is given sufficient velocity so that the bob describe vertical circle whose radius equal to length of pendulum. The maximum difference in the kinetic energy of bob during one revolution is.

A
0.98 J
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B
1.96 J
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C
4.9 J
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D
9.8 J
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Solution

## The correct option is A 0.98 JA bob of mass m=0.05Kg is performing vertical circle of radius (r)=1m.In the boundary case.a minimum velocity of μ=√5gr has to provided to it so it completes a vertical circle.So, kinetic energy (K1) at the lowest point,K1=12mμ2=52mgrand PE=0, raking it as reference at highest pointPE:μ2=mgh=2mgr (ash=2r)From conservation of energy.K1+μ1=K2+μ2⇒K2=K1−μ2=12mgrThus, loss in KE:ΔK=K1−K2=2mgr=2×0.05×9.8×1=0.98J (Ans)

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