Two point-like objects of masses 20 gm and 30 gm are fixed at the two ends of a rigid massless rod of length 10 cm . This system is suspended vertically from a rigid ceiling using a thin wire attached to its center of mass, as shown in the figure. The resulting torsional pendulum undergoes small oscillations. The torsional constant of the wire is 1 . 2 × 10 − 8 N m rad − 1 . The angular frequency of

Step-by-step solution

Given: m 1 = 30   gm and m 2 = 20   gm . Moment of inertia about the axis of rotation is I = m 1 r 1 2 + m 2 r 2 2 X-coordinate of the centre of mass can be written as, x C M = m 1 x 1 + m 2 x 2 m 1 + m 2 = 0 + 20 × 10 - 3 × 10 × 10 - 2 30 × 10 - 3 + 20 × 10 - 3 = 4 × 10 - 2   m = 4   cm = r 1 Therefore, And r 2 = 10 - 4   cm = 6   cm ∴   I = 30 × 10 - 3 × 16 × 10 - 4 + 20 × 10 - 3 × 36 × 10 - 4 ⇒   I = 1