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A simple pendulum of length 1 feet suspe...

A simple pendulum of length 1 feet suspended from the ceiling of an elevator takes `pi/3` seconds to complete one oscilation. Find the acceleration of the elevator.

Text Solution

Verified by Experts

The correct Answer is:
`4(ft)/sec^2`
Let the elevator be moving upward acceleration `a_0`
Here driving force
`f=m(g-a_0)sintheta`
Acceleration `=(g+a_0)theta=(g-a_0)theta(sinthetararrtheta)`
`=((g+a_0)x)/l=omega^2x`
`T=2pisqrt(l/(g+a_0)`
Given that `T=pi/3 sec, l=1ft `
and `g=32(ft)/sec^2`
`=pi/3=2pisqrt(1/(32+a_0))`
`1/9=4(1/(32+a))`
`rarr 32+a=36`
`a=36-32=4(ft)/sec^2`
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