The period of a simple pendulum, whose bob is | vedclass

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Question

(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L_{eff}}{g}}$, where $L_{eff}$ is the distance from the point of suspension

Vedclass · Accepted Answer

$T = T_1 = T_2 < T_3$

Vedclass · Answer

(B) The time period of a simple pendulum is given by $T = 2\pi \sqrt{\frac{L_{eff}}{g}}$, where $L_{eff}$ is the distance from the point of suspension to the center of mass of the bob.For a hollow sphere, a sphere filled with sand, and a sphere completely filled with mercury, the center of mass is at the geometric center of the sphere.Thus, $L_{eff}$ is the same for $T$, $T_1$, and $T_2$, implying $T = T_1 = T_2$.When the sphere is half-filled with mercury, the center of mass shifts downwards from the geometric center.This increases the effective length $L_{eff}$, and since $T \propto \sqrt{L_{eff}}$, the time period $T_3$ becomes greater than $T$, $T_1$, and $T_2$.Therefore, $T = T_1 = T_2 < T_3$.

The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T$. The period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury, and $T_3$ when it is half-filled with mercury. Which of the following is true?

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