Question 91: Centre of Mass and Rotational Motion

Question

Two bodies of mass $$1 \mathrm{~kg}$$ and $$3 \mathrm{~kg}$$ 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 :

Accepted Answer

$${\overline r _{com}} = {{{m_1}{{\overline r }_1} + {m_2}{{\overline r }_2}} \over {{m_1} + {m_2}}}$$
$$ = {{(1 - 9)\widehat i + (2 - 6)\widehat j + (1 + 3)\widehat k} \over 4}$$
$$ = {{ - 8\widehat i - 4\widehat j + 4\widehat k} \over 4}$$
$${\overline r _{com}} =  - 2\widehat i - \widehat j + \widehat k$$
$$\left| {\overline r } \right| = \sqrt {4 + 1 + 1}  = \sqrt 6 $$
$$\left| {\widehat i + 2\widehat j + \widehat k} \right| = \sqrt 6 $$

Answer

$$\hat{i}+2 \hat{j}+\hat{k}$$

Answer

$$-3 \hat{i}-2 \hat{j}+\hat{k}$$

Answer

$$-2 \hat{i}+2 \hat{k}$$

Answer

$$2 \hat{i}-\hat{j}+2 \hat{k}$$

Centre of Mass and Rotational Motion

Two bodies of mass $1 \mathrm{~kg} and 3 \mathrm{~kg} have position vectors \hat{i}+2 \hat{j}+\hat{k} and -3 \hat{i}-2 \hat{j}+\hat{k}$ 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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