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A simple pendulum is oscillating with an angular amplitude of 90o as shown in fig. (4). The value of θ for

which the resultant acceleration of the bob is directed horizontally is

a
0∘
b
90∘
c
sin−1⁡(1/3)
d
cos−1⁡(1/3)

detailed solution

Correct option is D

See fig. (11).From figure     at=gsin⁡θand    ac=v2l=2glcos⁡θl=2gcos⁡θNow,    tan⁡θ=acsin⁡90∘at+accos⁡90∘or       tan⁡θ=2gcos⁡θgsin⁡θ=2tan⁡θor      tan2⁡θ=2  or  sec2⁡θ=3∴ cos⁡θ=1/3θ=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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