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Questions  

A bob of mass m is attached to one end of a string of length l. This is kept in the horizontal position and released from the rest. At what angle from vertical will the tension in the string be equal to the weight in magnitude ?

a
cos−1⁡12
b
cos−1⁡13
c
cos−1⁡(1/2)
d
cos−1⁡(1/3)

detailed solution

Correct option is B

From figure,  T−mgcos⁡θ=mv2l∴ T=mgcos⁡θ+mv2/l or  mg=mgcos⁡θ+mv2/l or  mg=mgcos⁡θ+ml(2g)(l−h)∴ 1=cos⁡θ+2cos⁡θ1=3cos⁡θ∴ cos⁡θ=1/3 or θ=cos−1⁡(1/3)

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A pendulum of length / = l m is released from θ0 = 600. The rate of change of speed of the bob at θ = 300 is (g = 10 m/s2)


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