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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA couple consists of two forces \( \mathbf{F}_1 = (2\hat{i} + 3\hat{j} - \hat{k})\text{ N} \) acting at point \( A(1, -1, 2)\text{ m} \) and \( \mathbf{F}_2 = (-2\hat{i} - 3\hat{j} + \hat{k})\text{ N} \) acting at point \( B(3, 2, -1)\text{ m} \). The magnitude of the moment of this couple is:
Correct answer · Option 3
\( 2\sqrt{13}\text{ N m} \)
Explanation
Moment of couple \( \boldsymbol{\tau} = (\mathbf{r}_A - \mathbf{r}_B) \times \mathbf{F}_1 = (-2\hat{i} - 3\hat{j} + 3\hat{k}) \times (2\hat{i} + 3\hat{j} - \hat{k}) = -6\hat{i} + 4\hat{j} + 0\hat{k}\text{ N m} \). Magnitude is \( \sqrt{(-6)^2 + 4^2} = \sqrt{52} = 2\sqrt{13}\text{ N m} \).
