CONCEPT:
Equilibrium of a rigid body:
- A rigid body is said to be in mechanical equilibrium if both its linear momentum and angular momentum are not changing with time, or equivalently, the body has neither linear acceleration nor angular acceleration.
- Condition for the mechanical equilibrium:
- The total force, i.e. the vector sum of the forces, on the rigid body is zero.
- The total torque, i.e. the vector sum of the torques on the rigid body is zero.
⇒ \(\rm\vec{F_1}+\vec{F_2}+...+\vec{F_n}=0\)
⇒ \(\rm \vec{τ_1}+\vec{τ_2}+...+\vec{τ_n}=0\)
- If the forces on a rigid body are acting in the 3 dimensions, then six independent conditions to be satisfied for the mechanical equilibrium of a rigid body.
- If all the forces acting on the body are coplanar, then we need only three conditions to be satisfied for mechanical equilibrium.
- A body may be in partial equilibrium, i.e., it may be in translational equilibrium and not in rotational equilibrium, or it may be in rotational equilibrium and not in translational equilibrium.
EXPLANATION:
- A rigid body is said to be in mechanical equilibrium if both its linear momentum and angular momentum are not changing with time, or equivalently, the body has neither linear acceleration nor angular acceleration.
- We know that the linear acceleration and the angular acceleration of a stationary body are zero.
A book is kept on a table:
- In this case, the book will be stationary so it is an example of the equilibrium of a body.
A ball is moving downward freely under gravity:
- We know that when a ball moves freely under gravity, then only the gravitational force will act on the ball due to which the ball accelerates downward.
- Therefore ball is moving downward freely under gravity is not an example of the equilibrium of a body.
- Hence, option 1 is correct.
