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If the velocity of a rotating body of mass 50 kg is given by $\bar{V} = 3 \bar{i} + 4 \bar{j} + 5 \bar{k}$ and radius vector $\bar{r} = 2 \bar{i} + 3 \bar{j} + 4 \bar{k}$ , then its angular momentum is.

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50 \bar{i} + 50 \bar{j} + 50 \bar{k}

50 \bar{i} + 100 \bar{j} + 50 \bar{k}

50 \bar{i} + 50 \bar{j} + 100 \bar{k}

- 50 \bar{i} + 100 \bar{j} - 50 \bar{k}

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detailed solution

Correct option is D

Angular momentum is given as $\bar{L} = m (\bar{r} x \bar{v})$

$\bar{r} x \bar{v} = |\begin{matrix} \hat{i} & \hat{j} & \hat{k} \\ 2 & 3 & 4 \\ 3 & 4 & 5 \end{matrix}|$

$= \hat{i} (15 - 16) - \hat{j} (10 - 12) + \hat{k} (8 - 9) = - \hat{i} + 2 \hat{j} - \hat{k}$

$\bar{L} = m (\bar{r} x \bar{v}) = 50 (- \hat{i} + 2 \hat{j} - \hat{k}) = - 50 \hat{i} + 100 \hat{j} - 50 \hat{k}$

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2023 | www.infinitylearn.com

If the velocity of a rotating body of mass 50 kg is given by V¯=3i¯+4j¯+5k¯ and radius vector r¯=2i¯+3j¯+4k¯, then its angular momentum is.

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If the velocity of a rotating body of mass 50 kg is given by $\bar{V} = 3 \bar{i} + 4 \bar{j} + 5 \bar{k}$ and radius vector $\bar{r} = 2 \bar{i} + 3 \bar{j} + 4 \bar{k}$ , then its angular momentum is.