Determine the time period of small oscillations for a metre stick that is suspended from its 20 cm mark.

Step-by-step solution

Length of the metre stick, L = 1 m Distance of the center of mass from the point of suspension, d = 50 cm - 20 cm = 30 cm = 0.3 m Moment of inertia of the metre stick about the point of suspension is given by the parallel axis theorem: I = I_ CM + M d^2 = M L^2 12 + M d^2 I = M ( 1^2 12 + (0.3)^2 ) = M ( 1 12 + 9 100 ) = M ( 25 + 27 300 ) = 52 M 300 = 13 M 75 The time period of a physical pendulum is: T = 2 I M g d Substituting the values and taking g = 10 m/s ^2 : T = 2 13 M 75 M 10 0.3 = 2 13 75 3 = 2 13 225 = 2