Two point masses `m_(1)` and `m_(2)` are fixed to a light rod hinged at one end. The masses are at distances `l_(1)` and `l_(2)` repsectively from the hinge. Find the time period of oscillation (small amplitude) of this system in seconds if `m_(1) = m_(2), l_(1) = 1m, l_(2) = 3m`. If the time period is `xpi`, then find `x`.

Answer

1

Explanation

Net rostoring about `O`
`= m_(1)gl_(1) sintheta + m_(2)gl_(2) sintheta = (m_(1)l_(1) + m_(2)l_(2))g sintheta`
`rArr tau_("restoring") = (m_(1)l_(1) + m_(2)l_(2))g sintheta`
compare with `tau = Ctheta`
`T = 2pi sqrt((I_(o))/(C)) = 2pisqrt(((m_(1)l_(1)^(2) + m_(2)l_(2)^(2)))/((m_(1)l_(1)^(2) + m_(2))g))= 1 pi`.