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When no external torque acts on a system, the angular momentum remains conserved. Which of the following statements is correct in this context?

1. For a rotating body, the relationship between initial and final moments of inertia and angular velocities is given by: I₁ω₁ = I₂ω₂, where I₂ can be expressed as MR² or MR² + 2mR².
2. The torque is defined as the cross product of position vector and force, τ = r × F, which implies that τ · r = 0.
3. The radial force component does not generate torque, while the transverse force component is responsible for producing torque.
4. The torque produced by the weight of a rod is given by τ = mg × (ℓ/2).

Correct answer: The radial force component does not generate torque, while the transverse force component is responsible for producing torque.

Solution

Option C is correct because the radial component of force does not create a torque as it acts along the line of the radius vector, while the transverse component contributes to torque by being perpendicular to the radius vector.

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