(B) The initial velocity of the centre of mass $(V_{cm})$ is given by:$V_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} = \frac{1 \times 4 + 2 \times 0}{1

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The centre of mass first moves up and then comes down.

(B) The initial velocity of the centre of mass $(V_{cm})$ is given by:$V_{cm} = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} = \frac{1 \times 4 + 2 \times 0}{1 + 2} = \frac{4}{3}\, m/s$ (upwards).Since both balls are under the influence of gravity,the acceleration of each ball is $g$ downwards.The acceleration of the centre of mass $(a_{cm})$ is given by:$a_{cm} = \frac{m_1 a_1 + m_2 a_2}{m_1 + m_2} = \frac{1 \times (-g) + 2 \times (-g)}{1 + 2} = -g$ (downwards).Since the centre of mass has an initial upward velocity and a constant downward acceleration,it will first move up,reach a maximum height,and then come down.

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

Medium

$A$ ball of mass $1\, kg$ is thrown up with an initial speed of $4\, m/s$. $A$ second ball of mass $2\, kg$ is released from rest from some height as shown in the figure. Select the correct alternative.

A
The centre of mass of the two balls comes down with acceleration $g/3$.
B
The centre of mass first moves up and then comes down.
C
The acceleration of the centre of mass is first $g$ downwards and then $g$ upwards.
D
The centre of mass of the two balls remains stationary.

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System of Particles and Rotational Motion

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Motion of Centre of Mass

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Two particles of equal mass have velocities $\overrightarrow{v}_1=4 \hat{i} \text{ ms}^{-1}$ and $\overrightarrow{v}_2=4 \hat{j} \text{ ms}^{-1}$. The first particle has an acceleration $\overrightarrow{a}_1=(5 \hat{i}+5 \hat{j}) \text{ ms}^{-2}$ while the acceleration of the other particle is zero. The centre of mass of the two particles moves in a path of

DifficultAP EAMCET 2004

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Two bodies of masses $m_1$ and $m_2$ $(m_1 > m_2)$ are tied to the ends of a string which passes over a light frictionless pulley. The masses are initially at rest and then released. The acceleration of the centre of mass is

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$A$ ball of mass $1\, kg$ is thrown up with an initial speed of $4\, m/s$. $A$ second ball of mass $2\, kg$ is released from rest from some height as shown in the figure. Select the correct alternative.

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Two bodies of $6 \,kg$ and $4 \,kg$ masses have their velocities $5 \hat{i}-2 \hat{j}+10 \hat{k}$ and $10 \hat{i}-2 \hat{j}+5 \hat{k}$ respectively. Then the velocity of their centre of mass is

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