In the given figure: (a) if ball performs pure rolling then...

In the given figure:
(a) if ball performs pure rolling then friction in surface is absent
(b) if air resistance is absent, after point $A$, angular momentum of ball remains constant
(c) after $A$, path of centre of mass is parabolic
(d) both (b) and (c) are correct

Key Concepts

Projectile Motion

Projectile motion refers to the trajectory of an object that is moving under the influence of gravity alone after being projected into the air. In such a scenario, if air resistance is negligible, the object’s center of mass follows a parabolic path determined solely by its initial velocity and the acceleration due to gravity.

Pure Rolling Motion

Pure rolling motion is a type of movement where an object rotates while simultaneously translating such that the point of contact with the surface is momentarily at rest relative to the surface. This condition prevents slipping and ensures a fixed relation between the translational speed and the angular speed of the object.

Static Friction

Static friction is the force that acts at the point of contact between a rolling object and the surface to prevent relative motion (slipping). Although it can be essential for initiating and maintaining pure rolling by providing the necessary torque, static friction does not perform work since there is no displacement at the point where it applies.

Angular Momentum Conservation

Angular momentum conservation is a principle stating that in the absence of an external torque, the total angular momentum of a system remains constant over time. This concept is particularly relevant in situations where an object is no longer subjected to influence from forces that can exert a net torque, leading to a constant angular momentum state.

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