A weightless rod of length l carries two equal masses m one...

A weightless rod of length $l$ carries two equal masses $m$ one fixed at the end and other in the middle of the rod. The rod can revolve in a vertical plane about $A$. Then horizontal velocity which must be imparted to end $C$ of rod to deflectit to horizontal position is: (a) $\sqrt{\frac{12}{5} g l}$ (b) $\sqrt{3 g} l$ (c) $\sqrt{\frac{16}{5} g l}$ (d) $\sqrt{2 g} \bar{l}$

A weightless rod of length $l$ carries two equal masses $m$ one fixed at the end and other in the middle of the rod. The rod can revolve in a vertical plane about $A$. Then horizontal velocity which must be imparted to end $C$ of rod to deflectit to horizontal position is:
(a) $\sqrt{\frac{12}{5} g l}$
(b) $\sqrt{3 g} l$
(c) $\sqrt{\frac{16}{5} g l}$
(d) $\sqrt{2 g} \bar{l}$

Key Concepts

Physical Pendulum

A physical pendulum is a rigid body that swings about a pivot under the influence of gravity. Analyzing its motion involves considering the distribution of mass (through the moment of inertia), energy conversions between kinetic and potential energy, and the dynamics of rotational motion, making it a key concept in understanding the behavior of extended objects in a gravitational field.

Rotational Kinematics

Rotational kinematics deals with the motion of bodies rotating about an axis, linking angular displacement, angular velocity, and angular acceleration. It helps in translating quantities like the tangential velocity at a point on a rotating body into the corresponding angular velocity of the system, which is essential in analyzing problems where a point on the body is given an initial speed.

Conservation of Energy

This principle asserts that energy in an isolated system remains constant over time. In rotational dynamics, it is used to relate the initial kinetic energy imparted to a system with the gravitational potential energy it gains as it rotates, thereby allowing the determination of required velocities or accelerations.

Moment of Inertia

The moment of inertia quantifies a body's resistance to changes in its rotational state, depending on the mass distribution relative to the axis of rotation. In problems involving rods, masses, or any extended bodies, calculating the moment of inertia is critical to understanding how imparted forces or velocities affect angular motion.

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