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The torque caused by the weight of the rod is given by which of the following expressions?

1. \( \tau = mg \times \frac{\ell}{2} \)
2. \( \tau = I \alpha \)
3. \( \alpha = \frac{3g}{2\ell} \)
4. \( \alpha = \frac{mg \times \ell}{2} \)

Correct answer: \( \tau = mg \times \frac{\ell}{2} \)

Solution

The weight of the rod acts at its center of mass, which is located at a distance of \( \frac{\ell}{2} \) from the pivot. The torque due to the weight is given by \( \tau = mg \times \frac{\ell}{2} \).

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