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Physics · SYSTEMS OF PARTICLES AND ROTATIONAL MOTION
हिन्दीA system consists of two particles: particle 1 of mass \( 1\,\text{kg} \) at \( \mathbf{r}_1 = (2\hat{i} + 3\hat{j})\,\text{m} \) moving with velocity \( \mathbf{v}_1 = (4\hat{i})\,\text{m/s} \), and particle 2 of mass \( 2\,\text{kg} \) at \( \mathbf{r}_2 = (\hat{i} - \hat{j})\,\text{m} \) moving with velocity \( \mathbf{v}_2 = (3\hat{j})\,\text{m/s} \). The total angular momentum of the system about the origin is:
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Correct answer · Option D
\( -6\hat{k}\,\text{kg}\cdot\text{m}^2/\text{s} \)
Explanation
\( \mathbf{l}_1 = \mathbf{r}_1 \times (m_1 \mathbf{v}_1) = (2\hat{i} + 3\hat{j}) \times (4\hat{i}) = -12\hat{k} \). For particle 2, \( \mathbf{p}_2 = 2(3\hat{j}) = 6\hat{j} \), so \( \mathbf{l}_2 = (\hat{i} - \hat{j}) \times (6\hat{j}) = 6\hat{k} \). Total angular momentum \( \mathbf{L} = \mathbf{l}_1 + \mathbf{l}_2 = -12\hat{k} + 6\hat{k} = -6\hat{k}\,\text{kg}\cdot\text{m}^2/\text{s} \).
