1.

Pendulum `A` is a physical pendulum made from a thin, rigid and uniform rod whose length is `d`. One end of this rod is attached to the ceiling by a frictionless hinge, so that the rod is free to swing back and forth. Pendulum `B` is a simple pendulum whose length is also `d`. Obtain the ratio `(T_(A))/(T_(B))` of their periods for small angle oscillations.

Answer» Correct Answer - A
`T_(A) = 2pi sqrt ((I)/(mgl))`
`= 2pi sqrt (((md^(2)//3))/(mg(d//2))) = ((sqrt2)/(3))2pi sqrt((d)/(g))`
and `T_(B) = 2pi sqrt((d)/(g))`
`:. (T_(A))/(T_(B)) = sqrt((2)/(3)) = 0.816`


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