Two bodies of mass 1 kg and 3 kg have position vectors i + 2j + k and -3i - 2j + k, respectively. The center of mass of this system has a position vector: (a) -2i - j + k (b) 2i - j - 2k (c) -i + j + k (d) -2i + 2k

Answer: (a). rcm = (m₁ r₁ + m₂ r₂)/(m₁ + m₂) = ((i + 2j + k) + 3(-3i - 2j + k))/(4) = (-8i - 4j + 4k)/(4) So the answer is (a) -2i - j + k.

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Q21NEET 2009 · AIPMTEasy

Centre of Mass of Discrete Particles

Two bodies of mass 1 kg and 3 kg have position vectors $\hat{i} + 2\hat{j} + \hat{k}$ and $-3\hat{i} - 2\hat{j} + \hat{k}$ , respectively. The center of mass of this system has a position vector:

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Answer: (a)

$\vec{r}_{cm} = \frac{m_1 \vec{r}_1 + m_2 \vec{r}_2}{m_1 + m_2}$
$= \frac{(\hat{i} + 2\hat{j} + \hat{k}) + 3(-3\hat{i} - 2\hat{j} + \hat{k})}{4} = \frac{-8\hat{i} - 4\hat{j} + 4\hat{k}}{4}$
So the answer is (a) $-2\hat{i} - \hat{j} + \hat{k}$ .

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