A weightless rigid rod with a small iron bob at the end is hinged at point A by a ball and socket joint 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 20 cm , fixed at its midpoint. The bob is displaced slightly, perpendicular to the plane of the figure. If the period of small oscillations of the system is x π 10 s , then wha

Step-by-step solution

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 m g cos θ . If the length AD is equal to L , then the length CD = L sin θ . T = 2 π L sin θ g   c o s θ T = 2 π L tan θ g   T = 2 π 2 l g   = 2 π 5 = 4 π 10 ⇒ x = 4