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Two blocks of masses 10 kg and 30 kg are placed on a straight line with coordinates (0,0) cm and (x,0) cm. The 10 kg block is moved 6 cm towards the other. The distance the 30 kg block must be moved to keep the centre of mass unchanged is

Asked in JEE Main 27th June 1st Shift 2022 · Discrete systems and motion of the centre of mass

• (1) 4 cm towards the 10 kg block
• (2) 2 cm away from the 10 kg block
• (3) 2 cm towards the 10 kg block
• (4) 4 cm away from the 10 kg block

Step-by-step solution

Why the other options are wrong

• (1) Comes from using m₁ d₁=m₂ d₂ but with the masses swapped, giving 30×6/10… mis-scaled to 4.
• (2) Right size but wrong direction: the 30 kg must move the same way the 10 kg moved, not opposite.
• (4) Wrong size and wrong direction, from swapping the masses and reversing the sense.

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