Consider the following statements about mechanics: 1. There is no net moment (torque) on a rigid body which is in equilibrium. 2. The momentum of a single body is always conserved in all situations. 3. The kinetic energy of an object is always conserved in all interactions. Which of the statements given above is or are correct?

Introduction / Context:

Classical mechanics deals with equilibrium, conservation laws and energy changes. This question tests your understanding of when torques, momentum and kinetic energy are conserved, and in what sense. It presents three statements and asks which are correct, focusing on the conditions for equilibrium and conservation.

Given Data / Assumptions:

• We consider rigid bodies and particles in Newtonian mechanics.
• Equilibrium implies no change in the state of motion of the body.
• Conservation of momentum is considered in the presence or absence of external forces.
• Conservation of kinetic energy is considered in various interactions or collisions.

Concept / Approach:

For a rigid body to be in complete mechanical equilibrium, two conditions must hold: the net force acting on it must be zero, and the net moment (or net torque) about any point must also be zero. Thus statement 1 is correct. Momentum conservation applies to an isolated system with no external net force; the momentum of an individual body can change due to forces from other bodies, so statement 2 is generally false. Kinetic energy is conserved only in perfectly elastic collisions; in inelastic processes it is not conserved, so statement 3 is also false. Therefore, only statement 1 is correct.

Step-by-Step Solution:

Verification / Alternative check:

Think of a block on a table at rest. The net force is zero (weight balanced by normal reaction) and the net torque about any point is also zero, satisfying statement 1. Now imagine a ball falling under gravity; its momentum clearly changes with time, contradicting statement 2. For statement 3, consider a perfectly inelastic collision where two objects stick together; the kinetic energy decreases and is partly converted into heat and deformation, showing that kinetic energy is not always conserved.

Why Other Options Are Wrong:

Option A: 1, 2 and 3 claims that momentum and kinetic energy are always conserved individually, which is false.

Option B: 2 and 3 only ignores the correct statement 1 and incorrectly accepts both 2 and 3.

Option C: 1 and 2 only wrongly accepts the idea that the momentum of a single body is always conserved.

Common Pitfalls:

Students sometimes misapply conservation laws, forgetting the requirement of isolation and absence of external forces. Momentum conservation always applies to a closed system, not necessarily to each body inside it. Similarly, mechanical energy and kinetic energy are conserved only in certain idealised interactions. Distinguishing between system level conservation and single body changes is essential to answer such questions correctly.

Final Answer:

The correct choice is 1 only.