Question

The velocities of three particles of masses 20g, 30g and 50 g are $10\overrightarrow{i},10\overrightarrow{j},\text{and}10\overrightarrow{k}$ respectively. The velocity of the centre of mass of the three particles is

• A. $2\overrightarrow{i} + 3\overrightarrow{j} + 5\overrightarrow{k}$
• B. $10(\overrightarrow{i} + \overrightarrow{j} + \overrightarrow{k})$
• C. $20\overrightarrow{i} + 30\overrightarrow{j} + 5\overrightarrow{k}$
• D. $2\overrightarrow{i} + 30\overrightarrow{j} + 50\overrightarrow{k}$

Answer 1

Answer: (A)

$2\overrightarrow{i} + 3\overrightarrow{j} + 5\overrightarrow{k}$

Answer 2

Velocity of centre of mass $v_{cm} = \frac{m_{1}v_{1} + m_{2}v_{2} + m_{3}v_{3}}{m_{1} + m_{2} + m_{3}} = \frac{20 \times 10\widehat{i} + 30 \times 10\widehat{j} + 50 \times 10\widehat{k}}{100} = 2\widehat{i} + 3\widehat{j} + 5\widehat{k}$.