# After freezing a pendulum

A light metal rod of length $$L$$ is pivoted at one end. A hollow sphere filled with water has mass $$M$$ and radius $$R<L$$ is attached to the free end of the rod. The rod-sphere system performs angular SHM in vertical plane after being released from angle $$\theta$$ with vertical as shown in the figure. Consider two cases

Case-1 : the water in the sphere is at $$5^\circ C$$
Case-2 : the water in the sphere is at $$-2^\circ C$$

Which of the following statements are true? [Neglect the expansion of volume of water on freezing]

A) Restoring torque in case 1 = Restoring torque in case 2.
B) Restoring torque in case 1 < Restoring torque in case 2.
C) Angular frequency for case 1 > Angular frequency for case 2.
D) Angular frequency for case 1 < Angular frequency for case 2.
E) Angular frequency for case 1 = Angular frequency for case 2.

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