(B) Since there is no external horizontal force acting on the system,the position of the center of mass remains constant.The center of mass $X_{cm}$ i

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(B) Since there is no external horizontal force acting on the system,the position of the center of mass remains constant.The center of mass $X_{cm}$ is given by the formula: $X_{cm} = \frac{M_1 x_1 + M_2 x_2}{M_1 + M_2}$.Here,$M_1 = M$,$x_1 = 0$,$M_2 = M$,and $x_2 = 10\, m$.$X_{cm} = \frac{M(0) + M(10)}{M + M} = \frac{10M}{2M} = 5\, m$.As the man pulls the rope,both move towards each other and meet at the center of mass position,which is $x = 5\, m$.

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

Medium

$A$ cart of mass $M$ is tied to one end of a massless rope of length $10\, m$. The other end of the rope is held by a man of mass $M$. The entire system is on a smooth horizontal surface. The man is at $x = 0$ and the cart is at $x = 10\, m$. If the man pulls the cart by the rope,the man and the cart will meet at the point:

A
$x = 0$
B
$x = 5\, m$
C
$x = 10\, m$
D
They will never meet

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Class 11

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System of Particles and Rotational Motion

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Motion of Centre of Mass

Two masses $m_1$ and $m_2$ start to move towards each other due to mutual gravitational force. If the distance covered by $m_1$ is $x$,then the distance covered by $m_2$ is:

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

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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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Two particles have masses $m_1$ and $m_2$. If the first particle $(m_1)$ is moved by a distance $d$ towards the center of mass,by what distance should the second particle $(m_2)$ be moved so that the center of mass of the system remains at the same position?

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The figure shows a man of mass $m$ standing at the end $A$ of a trolley of mass $M$ placed at rest on a smooth horizontal surface. The man starts moving towards the end $B$ with a velocity $u_{rel}$ with respect to the trolley. The length of the trolley is $L$. Choose the correct statement.

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