Q.

A particle falls freely near the surface of the earth. Consider a fixed point O (not vertically below the particle) on the ground. Then pickup the incorrect alternative or alternatives.

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a

The magnitude of angular momentum of the particle about O is increasing

b

The magnitude of torque of the gravitational force on the particle about O is decreasing

c

The moment of inertia of the particle about O is decreasing

d

The magnitude of angular velocity of the particle about O is increasing

answer is B.

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Detailed Solution

The magnitude of angular momentum of particle about O=mvdSince speed v of particle increases, its angular momentum about O increases. Magnitude of torque of gravitational force about O=mgd ⇒ torque is constant.Moment of inertia of particle about O=mr2 Hence MI of particle about O decreases. Angular velocity of particle about O=vsinθr∵v and sinθ  increases and r decreases.Thus, angular velocity of particle about O increases.
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A particle falls freely near the surface of the earth. Consider a fixed point O (not vertically below the particle) on the ground. Then pickup the incorrect alternative or alternatives.