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Question

# A simple pendulum of length 40cm oscillates with an angular amplitude of 0.04 rad. Find the angular acceleration when the bob is in momentary rest. Take g=10m/s2.

A
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B
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C
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D
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Solution

## The correct option is B 1rad/s2Given:- Length of simple pendulum = 40cm Angular amplitude = 0.04 radTo find:- The angular acceleration. Solution:-The angular frequency is ω=√glω=√10m/s20.4mω=5sec−1the time period is2πω=2π5sec−1=1.26sec.Linear amplitude = 40cm×0.04=1.6cmAngular speed at displacement 0.02 rad isω=(5sec−1)√(0.042)−(0.022)rad=0.17rad/secwhere speed of the bob at this instant=(40cm)×(0.175)−1=6.8cm/secAt momentary rest, the bob is in extreme position.Thus, the angular accelerationα=(0.4rad)(25sec2)=1rad/sec2Hence the correct option is C

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