After freezing a pendulum
A light metal rod of length
is pivoted at one end. A hollow sphere filled with water has mass
and radius
is attached to the free end of the rod. The rod-sphere system performs angular SHM in vertical plane after being released from angle
with vertical as shown in the figure. Consider two cases
Case-1 : the water in the sphere is at
Case-2 : the water in the sphere is at
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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1 solution
The torque is independent of moment of inertia which increases on freezing(since volume of ice is more than water it gets more spreaded and so more moment of inertia..the same reason why solid sphere has less moment of inertia than a hollow sphere)and hence w decreases .Torque is simply F×D .