Correct Answer - Option 3 : Both 1 and 2
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.
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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.
\(⇒ \vec{F_1}+\vec{F_2}+...+\vec{F_n}=0\)
\(⇒ \vec{τ_1}+\vec{τ_2}+...+\vec{τ_n}=0\)
- 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:
- We know that the momentum of a body is given as,
⇒ P = m × v -----(1)
Where m = mass, and v = velocity of the body
- From the above equation, it is clear that if the momentum of a body is constant, then its velocity will also be constant and the acceleration will be zero.
- 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.
- Therefore if a body is in equilibrium, then its acceleration will be zero.
- We know that whether the body is at rest or is moving with constant velocity, its acceleration in both cases will be zero. Hence, option 3 is correct.
