A child is standing at one end of a long trol | vedclass

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(D) The system consists of the child and the trolley. Since the floor is smooth,there is no external horizontal force acting on the system. According

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$v$

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(D) The system consists of the child and the trolley. Since the floor is smooth,there is no external horizontal force acting on the system. According to the law of conservation of momentum,the velocity of the centre of mass of a system remains constant if the net external force acting on it is zero. Initially,the trolley and the child are moving together with a speed $v$. Therefore,the initial velocity of the centre of mass is $v$. As the child starts running,the forces involved (the child pushing the trolley and the trolley pushing the child) are internal forces. Since internal forces do not change the velocity of the centre of mass,the centre of mass of the system will continue to move with the same speed $v$.

List-$I$	List-$II$
$(1)$ Planck's constant	$(i)$ $[ML^{-1} T^{-2}]$
$(2)$ Gravitational constant	(ii) $[ML^{-1} T^{-1}]$
$(3)$ Bulk modulus	(iii) $[ML^2 T^{-1}]$
$(4)$ Coefficient of viscosity	(iv) $[M^{-1} L^3 T^{-2}]$

$A$ child is standing at one end of a long trolley moving with a speed $v$ on a smooth horizontal floor. If the child starts running towards the other end of the trolley with a speed $u$,the centre of mass of the system (trolley + child) will move with a speed.

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