A weightless rigid rod with a small iron bob at the end is hinged at point A to the wall so that it can rotate in all directions. The rod is kept in the horizontal position by a vertical inextensible string of length `20cm`, fixed at its midpoint. The bob is displaced slightly perpenducular to the plane of the rod and string. Find period of small oscillations of the system in the form `(piX)/(10)s` and fill the value of X.

Answer

4

Explanation

The small oscillation of the bob occur relative to a stationary axis passing through AB. The line CD is perpendicular to the axis AB. The bob behaves as a simple pendulum of length CD oscillating due to component of its weight `mg cos theta`

If the length AD is equal to L, then the
length `CD=L sin theta`
`T=2pisqrt((L sin theta)/(g cos theta))`
`T=2pisqrt((L tan theta)/2)`
`T=2pisqrt((2l)/g)=(2pi)/5=(4pi)/10`
`impliesx=4`