(A) Given masses are $m_1 = 20 \ g$,$m_2 = 30 \ g$,$m_3 = 50 \ g$.Velocities are $v_1 = 10 \hat{i} \ m/s$,$v_2 = 10 \hat{j} \ m/s$,$v_3 = 10 \hat{k} \

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

(A) Given masses are $m_1 = 20 \ g$,$m_2 = 30 \ g$,$m_3 = 50 \ g$.Velocities are $v_1 = 10 \hat{i} \ m/s$,$v_2 = 10 \hat{j} \ m/s$,$v_3 = 10 \hat{k} \ m/s$.The velocity of the centre of mass $(v_{cm})$ is given by the formula:$v_{cm} = \frac{m_1 v_1 + m_2 v_2 + m_3 v_3}{m_1 + m_2 + m_3}$Substituting the values:$v_{cm} = \frac{20 \times 10 \hat{i} + 30 \times 10 \hat{j} + 50 \times 10 \hat{k}}{20 + 30 + 50}$$v_{cm} = \frac{200 \hat{i} + 300 \hat{j} + 500 \hat{k}}{100}$$v_{cm} = 2 \hat{i} + 3 \hat{j} + 5 \hat{k}$

Class 11 Physics System of Particles and Rotational Motion Centre of mass (Point Mass)

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

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

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

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In general form,what are the coordinates of the centre of mass of a rigid body?

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