Question

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. 

(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 1

Correct option: (b) The magnitude of torque of the gravitational force on the particle about O is decreasing

Explanation:

If student will use angular momentum = mvr.

He/she may conclude answer (1) as r is decreasing angular momentum must decrease hence (1) is incorrect.

The magnitude of angular momentum of particle about O = mvd

Since speed v of particle increases, its angular momentum about O increases.

Magnitude of torque of gravitational force about O = mgd ⇒ constant 

Moment of inertia of particle about O = mr²

Hence MI of particle about O decreases.

Angular velocity of particle about O = vsinθ
  / r

∴ v and sin θ increases and r decreases.

∴ angular velocity of particle about O increases.