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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA system consists of three particles of masses \( 1\text{ kg} \), \( 2\text{ kg} \), and \( 3\text{ kg} \). At an instant, their position vectors (in meters) are given by \( \vec{r}_1 = t^2\hat{i} \), \( \vec{r}_2 = 2t\hat{j} \), and \( \vec{r}_3 = (3t - t^2)\hat{k} \). The magnitude of the net external force acting on the entire system at \( t = 2\text{ s} \) is:
Correct answer · Option 2
\( 2\sqrt{10}\text{ N} \)
Explanation
\( \vec{a}_1 = \frac{d^2\vec{r}_1}{dt^2} = 2\hat{i} \), \( \vec{a}_2 = 0 \), \( \vec{a}_3 = -2\hat{k} \). Thus \( \vec{F}_{\text{ext}} = m_1\vec{a}_1 + m_2\vec{a}_2 + m_3\vec{a}_3 = 1(2\hat{i}) + 3(-2\hat{k}) = 2\hat{i} - 6\hat{k} \). Magnitude \( |\vec{F}_{\text{ext}}| = \sqrt{2^2 + (-6)^2} = \sqrt{40} = 2\sqrt{10}\text{ N} \).
