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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीThe angular momentum of a system of particles varies with time as \( \mathbf{L}(t) = (4t^2\hat{i} - 6t\hat{j} + 2\hat{k})\,\text{kg}\cdot\text{m}^2/\text{s} \). What is the magnitude of the net external torque acting on the system at \( t = 1\,\text{s} \)?
Correct answer · Option 4
10 N·m
Explanation
Net external torque is \( \boldsymbol{\tau}_{\text{ext}} = \frac{d\mathbf{L}}{dt} = 8t\hat{i} - 6\hat{j} \). At \( t = 1\,\text{s} \), \( \boldsymbol{\tau} = 8\hat{i} - 6\hat{j} \). Magnitude is \( |\boldsymbol{\tau}| = \sqrt{8^2 + (-6)^2} = 10\,\text{N}\cdot\text{m} \).
