System of Particles and Rotational Motion - Result Question 6
6. 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 centre of mass of this system has a position vector:
(a) $-2 \hat{i}-\hat{j}+\hat{k}$
(b) $2 \hat{i}-\hat{j}-2 \hat{k}$
(c) $-\hat{i}+\hat{j}+\hat{k}$
(d) $-2 \hat{i}+2 \hat{k}$
[2009]
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Answer:
Correct Answer: 6. (a)
Solution:
- (a) The position vector of the centre of mass of two particle system is given by
$ \begin{aligned} & \vec{R} _{c m}=\frac{m_1 \vec{r} _1+m_2 \vec{r} _2}{(m_1+m_2)} \\ & =\frac{1}{4}[-8 \hat{i}-4 \hat{j}+4 \hat{k}]=-2 \hat{i}-\hat{j}+\hat{k} \end{aligned} $
