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Question
The net external torque on a system of particles about an axis is zero. Which of the following are compatible with it?
- The forces may be acting radially from a point on the axis.
- The forces may be acting on the axis of rotation.
- The forces may be acting parallel to the axis of rotation.
- The torque caused by some forces may be equal and opposite to that caused by other forces.
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Solution
a, b, c and d
Explanation:
We know that torque on a system of particles `τ = r xx F = F sin θ hatn)` ......(i)
Where, θ is the angle between r and F, and `hatn` is a unit vector perpendicular to both r and F.
- When forces act radially, θ = 0 hence |τ| = 0 .....[From equation (i)]
- When forces are acting on the axis of rotation, r = 0, |τ| = 0 ......[From equation (i)]
- When forces acting parallel to the axis of rotation θ = 0°, |τ| = 0 .....[From equation (i)]
- When torque by forces are equal and opposite, the, τnet = τ1 = τ2 = 0
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