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 pick up the correct alternative or alternatives.
A. Angular momentum of the particle about O is increasing.
B. The moment of inertia of the particle about O is decreasing.
C. The moment of inertia of the particle about O is increasing.
D. The angular velocity of the particle about O is increasing.

Answer 1

The above problem can be resolved using the mathematical formula for the angular momentum and the linear velocity of a particle, undergoing the free fall. This free fall causes an increase in the magnitude of linear velocity continuously, which causes the increased magnitude of the angular momentum.

Complete step by step answer:
The expression for the angular momentum is given as,
$L = mvr\sin \theta$ ………………………..(1)
Here, m is the mass of the particle, v is the linear velocity of the particle and r is the radius of path, travelled by the particle.
As the particles fall freely near the surface of earth, then the magnitude of linear velocity will keep on increasing due to the increased effect of gravitational acceleration. And as the linear velocity increases, the angular momentum will also increase.
The expression for the linear velocity is given as,
$v = \dfrac{\omega }{r}$
Here, $\omega$ is the magnitude of angular velocity
And as per the previous explanation, as the magnitude of linear velocity increases the corresponding magnitude of the angular velocity of the particles also increases.
Therefore, both the angular momentum and the angular velocity will increase about O and option (D) is correct.

Note: To resolve the given problem, the concept of angular momentum is required to remember. In addition to this, one must be clear about the important fundamentals related to the motion under free fall. And the impact of the gravity on the velocity of the object undergoing the freefall motion.