A particle of mass 2, kg located at position (hat{i} + hat{j}) m has a velocity 2( + hat{i} -

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6.System of Particles and Rotational Motion

medium

$A$ particle of mass $2\, kg$ located at the position $(\hat i + \hat j)$ $m$ has a velocity $2( + \hat i - \hat j + \hat k)m/s$. Its angular momentum about $z$ -axis in $kg-m^2/s$ is

A

$0$

B

$+8$

C

$12$

D

$-8$

Solution

The angular momentum about origin

$\overrightarrow{\mathrm{L}}=\overrightarrow{\mathrm{r}} \times \mathrm{m} \overrightarrow{\mathrm{v}}$

$\overrightarrow{\mathrm{L}}=(\hat{i}+\hat{j}) \times 4(\hat{i}-\hat{j}+\hat{k})$

$\overrightarrow{\mathrm{L}}=4(-\hat{\mathrm{k}}-\hat{\mathrm{j}}-\hat{\mathrm{k}}+\hat{\mathrm{i}})$

$\overrightarrow{\mathrm{L}}=4 \hat{\mathrm{i}}-4 \hat{\mathrm{j}}-8 \hat{\mathrm{k}}$

$\therefore \mathrm{L}_{\mathrm{z}}=-8 \mathrm{kg} \mathrm{m}^{2} / \mathrm{s}$

Standard 11

Physics

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