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A simple pendulum of length 1 m with a b...

A simple pendulum of length 1 m with a bob of mass m swings with an angular amplitude 30°. Then (g = 9.8 `ms^(-2)`)

A

time period of pendulum is 2 s

B

tension in the string is greater than mgcos `15^(@)` at angular displacement 15°

C

rate of change of speed at angular displacement 15° is g sin 15°

D

tension in the string is `mg cos 15^(@)` at angulardisplacement 15°

Text Solution

Verified by Experts

The correct Answer is:
B, C

Simle pendulum of length 1 m is called second.s pendulum whose time period is T =2s. But this time period is for small oscillations. In this case, angular amplitude is `30^(@)`. Therefore, time period wil not be 2s. At angular displacement `15^(@)`.
`T-mg cos 15^(@) =(mv^(2))/l`
or `T gt mg cos 15^(@)` and tangential acceleration `a = g sin 15^(@)` = rate of change of speed.
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