Q66 / 90 · JEE Main 2022 (29 Jul Shift 1) · Physics

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 magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :

Correct answer
A
$\hat{i} - 2 \hat{j} + \hat{k}$
B
$- 3 \hat{i} - 2 \hat{j} + \hat{k}$
C
$- 2 \hat{i} + 2 \hat{k}$
D
$- 2 \hat{i} - \hat{j} + 2 \hat{k}$

Solution

As we know, centre of mass is given by, ${\vec{r}}_{com} = \frac{\sum m_{i} {\vec{r}}_{i}}{\sum m_{i}}$
${\vec{r}}_{com} = \frac{m (\hat{ı} + 2 \hat{ȷ} + \hat{k}) + 3 m (- 3 \hat{ı} - 2 \hat{ȷ} + \hat{k})}{m + 3 m}$
${\vec{r}}_{com} = \frac{- 8 m \hat{ı} - 4 m \hat{ȷ} + 4 m \hat{k}}{4 m} = - 2 \hat{ı} - \hat{ȷ} + \hat{k}$
The magnitude of the position vector of the centre of mass is $\sqrt{2^{2} + 1^{1} + 1^{2}} = \sqrt{6}$ .
It is similar to the magnitude of the option A.

Hence, the correct answer is option: 'A'.

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

Solution

Relevant Questions

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 magnitude of position vector of centre of mass of this system will be similar to the magnitude of vector :