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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION

हिन्दी

In the system shown in the figure , two equal and opposite forces of magnitude \( F \) act at the ends A and B of a light rod of length \( 2a \). Which of the following conditions correctly characterizes the equilibrium state of this rod?

  1. The rod is in both translational and rotational equilibrium.
  2. The rod is in rotational equilibrium but not in translational equilibrium.
  3. The rod is neither in translational nor in rotational equilibrium.
  4. The rod is in translational equilibrium but not in rotational equilibrium.

Correct answer · Option 4

The rod is in translational equilibrium but not in rotational equilibrium.

Explanation

In Fig. 6.20(b), the net force is \( \sum \mathbf{F} = \mathbf{F} + (-\mathbf{F}) = 0 \), ensuring translational equilibrium. However, both forces produce torques in the same anticlockwise sense about the midpoint C, so the net torque is \( \sum \tau = 2Fa \neq 0 \), meaning it is not in rotational equilibrium.
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