Motion of Centre of Mass PYQs: JEE Mains Physics

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1. 1. Two blocks of masses \(2\) kg and \(1\) kg respectively, are tied to the ends of a string which passes over a light frictionless pulley as shown in the figure below. The masses are held at rest at the same horizontal level and then released. The distance traversed by the centre of mass in \(2\) s is _______ m. (Take \(g = 10\) m/s\(^2\))
   2026 Hard
2. 2. Two identical bodies \(A\) and \(B\) of equal masses have initial velocities \(\vec{v_1} = 4\hat{i}\) m/s and \(\vec{v_2} = 4\hat{j}\) m/s respectively. The body \(A\) has acceleration \(\vec{a_1} = 6\hat{i} + 6\hat{j}\) m/s\(^2\) while the acceleration of the other body \(B\) is zero. The centre of mass of the two bodies moves in __________ path. 2026 Hard
3. 3. Two blocks of masses \(10 \; kg\) and \(30 \; kg\) are placed on the same straight line with coordinates \((0,0) \; cm\) and \(( x , 0) \; cm\) respectively. The block of \(10 \; kg\) is moved on the same line through a distance of \(6 \; cm\) towards the other block. The distance through which the block of \(30 \; kg\) must be moved to keep the position of centre of mass of the system unchanged is 2022 Medium
4. 4. Two masses \(A\) and \(B ,\) each of mass \(M\) are fixed together by a massless spring. \(A\) force acts on the mass \(B\) as shown in figure. If the mass \(A\) starts moving away from mass \(B\) with acceleration \('a',\) then the acceleration of mass \(B\) wil be :-
   2021 Hard
5. 5. A boy of mass \(20\, kg\) is standing on a \(80\, kg\) free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing \(25\, m\) from a wall. If he walks \(10\, m\) on the cart towards the wall, then the final distance of the boy from the wall will be ........ \(m\) 2013 Hard
6. 6. A boy of mass \(20\, kg\) is standing on a \(80\, kg\) free to move long cart. There is negligible friction between cart and ground. Initially, the boy is standing \(25\, m\) from a wall. If he walks \(10\, m\) on the cart towards the wall, then the final distance of the boy from the wall will be ........ \(m\) 2013 Hard

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