JEE MAIN - Physics (2022 - 29th July Morning Shift - No. 6)
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 :
$$\hat{i}+2 \hat{j}+\hat{k}$$
$$-3 \hat{i}-2 \hat{j}+\hat{k}$$
$$-2 \hat{i}+2 \hat{k}$$
$$2 \hat{i}-\hat{j}+2 \hat{k}$$
Explanation
$${\overline r _{com}} = {{{m_1}{{\overline r }_1} + {m_2}{{\overline r }_2}} \over {{m_1} + {m_2}}}$$
$$ = {{(1 - 9)\widehat i + (2 - 6)\widehat j + (1 + 3)\widehat k} \over 4}$$
$$ = {{ - 8\widehat i - 4\widehat j + 4\widehat k} \over 4}$$
$${\overline r _{com}} = - 2\widehat i - \widehat j + \widehat k$$
$$\left| {\overline r } \right| = \sqrt {4 + 1 + 1} = \sqrt 6 $$
$$\left| {\widehat i + 2\widehat j + \widehat k} \right| = \sqrt 6 $$
Comments (0)
