1.

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))

Answer»

time period of pendulum is 2 s
tension in the string is greater than mgcos `15^(@)`at angular displacement 15°
RATE of change of speed at angular displacement 15° is g sin 15°
tension in the string is `mg cos 15^(@)`at angulardisplacement 15°

Solution :
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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