Match the following statements regarding the motion of the center of mass (COM) of a system. List - I List - II (P) Velocity of COM of a system of two blocks (mass m moving with velocity v , and stati

Question

Match the following statements regarding the motion of the center of mass (COM) of a system.

List - I	List - II
(P) Velocity of COM of a system of two blocks (mass $m$ moving with velocity $v$ , and stationary mass $2 m$ ) immediately after an inelastic collision.	(1) $0$
(Q) Displacement of COM of two particles of masses $m_{1}$ and $m_{2}$ initially at rest, moving under mutual attractive forces, after time $t$ .	(2) $\frac{v}{3}$
(R) Acceleration of COM of a system of three particles ( $m_{1}, m_{2}, m_{3}$ ) subjected to external forces $F_{1}, F_{2}, F_{3}$ respectively.	(3) $\frac{F _{1} + F _{2} + F _{3}}{m _{1} + m _{2} + m _{3}}$
(S) Horizontal velocity of COM of a block-wedge system (masses $m$ and $M$ respectively, all surfaces frictionless) when the block slides down the wedge.	(4) $v$

TestHub · Accepted Answer

For P, the initial momentum is m v . The total mass is m + 2 m = 3 m . The velocity of COM is V COM ​ = 3 m m v ​ = 3 v ​ . For Q, since the particles are initially at rest and move under mutual (internal) forces, the COM remains at rest, so its displacement is 0 . For R, the acceleration of COM is given by a COM ​ = M t o t a l ​ F e x t ​ ​ = m 1 ​ + m 2 ​ + m 3 ​ F 1 ​ + F 2 ​ + F 3 ​ ​ . For S, since there are no external horizontal forces on the block-wedge system, the horizontal momentum of the COM is conserved. As the system starts from rest, the horizontal velocity of the COM remains 0 .

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JEE Advanced 2028 (Class 11)