Question

A uniform plank of length l and mass m is balanced on a fixed semi cirxular plate of radius r ...

Answer 1

Answer:

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Explanation:

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Answer 2

Explanation:

The net torque acting on the bar about P when it is tilte through a small distance x (corresponding angle `theta`) is given as

`tau = - mg x cos theta`

`rArr -lp omega_(osc)^(2) theta = mg x`

`rArr - (m l^(2))/(12) omega_(osc)^(2) = mg R theta`

`cos theta ~= 1 " for small " theta & x = R theta " for small " theta`

`rArr omega_(osc) = sqrt((12gR)/(l^(2)))`

`rArr T = (2pi)/(omega) = (2pi l)/(omega) = (2pi l)/(sqrt(12gR)) = (pi l)/(sqrt(3gR))`