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Q.

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 ?

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a

cos−1⁡12

b

cos−1⁡13

c

cos−1⁡(1/2)

d

cos−1⁡(1/3)

answer is B.

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Detailed Solution

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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