A simple pendulum of length L and having a bob of mass m oscillates with a time period T₀ on the surface of Earth. The pendulum is then taken to a planet where the acceleration due to gravity is 1 16 of that on Earth. If the length of the pendulum is changed to 9 4 L and its bob is replaced by another bob of mass 4m , what will be the new time period of oscillation?

Step-by-step solution

The time period of a simple pendulum is given by the formula: T = 2 L g The time period is independent of the mass of the bob. Therefore, changing the mass from m to 4m has no effect on the time period. Initial time period on Earth is: T₀ = 2 L g On the new planet, the acceleration due to gravity is g' = g 16 and the new length of the pendulum is L' = 9 4 L . The new time period T' is: T' = 2 L' g' Substituting the values of L' and g' : T' = 2 9 4 L g 16 T' = 2 9 4 16 L g T' = 2 36 L g T' = 6 2 L g T' = 6 T₀ Answer