Two pendulums each consist of a solid uniform ball of mass M by a rigid, massles

Question

Two pendulums each consist of a solid uniform ball of mass M by a rigid, massless rod where the center of that mass is a distance L away. Pendulum A has mass M concentrated into a very small volume that distance L away from its axis. Pendulum B has the mass M spread out into a solid uniform ball of radius L/2. Which pendulum takes longer to oscillate? What is the period of oscillation for pendulum A, in terms m, L, g, and/or any constants? There is no need to write 'T=... Just enter the expression. What is the period of oscillation for pendulum B, in terms of m, g, and/or any constants?

Explanation / Answer

for pendulum A T= 2*pi(l/g)^(0.5) for pendulum B T = 2*pi*(I/mgh)^(0.5) where I is moment of inertia about suspended point I = 2/5*M*(L/2)^2 + M*L^2 = 11/10 ML^2 substituting we get T = 2*pi*((11/10)*(l/g))^(0.5) => pendulum B takes longer time

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