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JEE Main 2022 (29 Jul, Shift 1) · Centre of Mass of Discrete Particles

Centre of Mass of Discrete Particles question from JEE Main 2022 (29 Jul, Shift 1)

Q11JEE Main 2022 · 29 JUL · SHIFT 1Easy

Centre of Mass of Discrete Particles

Two bodies of mass $1\text{ kg}$ and $3\text{ kg}$ have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$ respectively. The magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector:

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Answer: (a)

$\vec{r}_{cm} = \frac{(\hat{i} + 2\hat{j} + \hat{k}) + 3(-3\hat{i} - 2\hat{j} + \hat{k})}{4} = -2\hat{i} - \hat{j} + \hat{k}$
$|\vec{r}_{cm}| = \sqrt{4 + 1 + 1} = \sqrt{6}$
$|\hat{i} + 2\hat{j} + \hat{k}| = \sqrt{1 + 4 + 1} = \sqrt{6}$
So the answer is (a) $\hat{i} + 2\hat{j} + \hat{k}$ .

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