Question

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

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

Answer 1

Answer: (A)

$2\overset{\land}{i} + 3\overset{\land}{j} + 5\overset{\land}{k}$

Answer 2

${\overset{\rightarrow}{v}}_{cm} = \frac{m_{1}{\overset{\rightarrow}{v}}_{1} + m_{2}{\overset{\rightarrow}{v}}_{2} + m_{3}{\overset{\rightarrow}{v}}_{3}}{m_{1} + m_{2} + m_{3}}$

$= \frac{20 \times 10\widehat{i} + 30 \times 10\widehat{j} + 50 \times 10\widehat{k}}{100}$

∴ $v_{cm} = 2\widehat{i} + 3\widehat{j} + 5\widehat{k}$ 7.