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A spherical bob of mass m and radius R i...

A spherical bob of mass m and radius R is attached to a fixed point by means of a massless rigid rod whose length from the point of support up to the centre of bob is l. Find the period of small oscillation.

Text Solution

Verified by Experts

`l (d^(2) theta)/(dt^(2)) = -mg l sin theta ~= -mg l theta`
where `l = (2)/(5) mR^(2) + m l^(2)`
`=m ((2)/(5) R^(2) + l^(2))`
`:. (d^(2) theta)/(dt^(2)) = (- mg l theta)/(m((2)/(5) R^(2) + l^(2)))`
`rArr T = 2pi sqrt((5l^(2) + 2R^(2))/(5gl))`
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