(C) The acceleration of the centre of mass is given by $a_{cm} = \frac{m_A a_1 + m_B a_2}{m_A + m_B}$.Since $m_A = m_B = m$,we have $a_{cm} = \frac{m(

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(C) The acceleration of the centre of mass is given by $a_{cm} = \frac{m_A a_1 + m_B a_2}{m_A + m_B}$.Since $m_A = m_B = m$,we have $a_{cm} = \frac{m(6\hat{i} + 6\hat{j}) + m(0)}{2m} = 3\hat{i} + 3\hat{j} \text{ m/s}^2$.The initial velocity of the centre of mass is $v_{cm} = \frac{m_A v_1 + m_B v_2}{m_A + m_B} = \frac{m(4\hat{i}) + m(4\hat{j})}{2m} = 2\hat{i} + 2\hat{j} \text{ m/s}$.Since the acceleration vector $a_{cm} = 3\hat{i} + 3\hat{j}$ and the initial velocity vector $v_{cm} = 2\hat{i} + 2\hat{j}$ are parallel (specifically,$a_{cm} = 1.5 v_{cm}$),the motion of the centre of mass is along a straight line.

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

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Two identical bodies $A$ and $B$ of equal masses have initial velocities $v_1 = 4\hat{i} \text{ m/s}$ and $v_2 = 4\hat{j} \text{ m/s}$ respectively. The body $A$ has acceleration $a_1 = 6\hat{i} + 6\hat{j} \text{ m/s}^2$ while the acceleration of the other body $B$ is zero. The centre of mass of the two bodies moves in . . . . . . path.

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circular
B
parabolic
C
straight line
D
elliptical

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Class 11

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Chapter

System of Particles and Rotational Motion

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Motion of Centre of Mass

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Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the center of mass of the system is,

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Two blocks of masses $5 \,kg$ and $2 \,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $7 \,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ....... $m/s$.

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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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Two particles of the same mass are moving towards each other with velocities $2v$ and $v$ respectively. The velocity of the centre of mass of the system is:

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Two blocks of masses $5 \, kg$ and $2 \, kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse provides a velocity of $7 \, m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ............ $m/s$.

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Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their speeds are $v$ and $2v$ at any instant,then the speed of the center of mass of the system is,

Two blocks of masses $5 \,kg$ and $2 \,kg$ are connected by a spring of negligible mass and placed on a frictionless horizontal surface. An impulse gives a velocity of $7 \,m/s$ to the heavier block in the direction of the lighter block. The velocity of the centre of mass is ....... $m/s$.

Two particles of the same mass are moving towards each other with velocities $2v$ and $v$ respectively. The velocity of the centre of mass of the system is:

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