(A) Let the velocity of the first particle be $\vec{v}_1 = 10 \hat{i} \text{ ms}^{-1}$ and the velocity of the second particle be $\vec{v}_2 = 5 \hat{

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(A) Let the velocity of the first particle be $\vec{v}_1 = 10 \hat{i} \text{ ms}^{-1}$ and the velocity of the second particle be $\vec{v}_2 = 5 \hat{j} \text{ ms}^{-1}$.The masses are $m_1 = 10 \text{ g}$ and $m_2 = 15 \text{ g}$.The velocity of the centre of mass $\vec{v}_{cm}$ is given by:$\vec{v}_{cm} = \frac{m_1 \vec{v}_1 + m_2 \vec{v}_2}{m_1 + m_2}$$\vec{v}_{cm} = \frac{10(10 \hat{i}) + 15(5 \hat{j})}{10 + 15} = \frac{100 \hat{i} + 75 \hat{j}}{25} = 4 \hat{i} + 3 \hat{j} \text{ ms}^{-1}$.The magnitude of the velocity of the centre of mass is:$|\vec{v}_{cm}| = \sqrt{4^2 + 3^2} = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ ms}^{-1}$.

Class 11 Physics System of Particles and Rotational Motion Motion of Centre of Mass

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$A$ particle of mass $10 \text{ g}$ is moving towards east with a velocity of $10 \text{ ms}^{-1}$ and another particle of mass $15 \text{ g}$ is moving towards north with a velocity of $5 \text{ ms}^{-1}$. The magnitude of the velocity of the centre of mass of the system of the two particles is (in $\text{ ms}^{-1}$)

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A
$5$
B
$10$
C
$15$
D
$7.5$

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System of Particles and Rotational Motion

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Motion of Centre of Mass

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