Consider a simple pendulum oscillating in a vacuum with a bob made of solid brass. If the brass bob is replaced by an identical hollow metallic bob of the same external dimensions filled completely with dense mercury, what happens to the time period of oscillation?

💡 Solution & Explanation

The time period of a simple pendulum depends solely on its effective length from the point of suspension to the center of mass and the acceleration due to gravity, as given by the formula T equals 2 pi times the square root of L over g. Since both external dimensions and total mass distribution yielding the center of mass remain unchanged, the time period stays constant. Alterations in mass alone do not affect the simple pendulum period in the absence of air resistance. The center of mass of both solid and filled hollow spheres of identical outer radii coincides.