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Two blocks of masses $40 kg$ and $25 kg$ are placed on the same straight line with coordinates $(0, 0) cm$ and $(50, 0) cm$ respectively. The block of $40 kg$ is moved on the same line through a distance of $5 cm$ towards the other block. The distance through which the block of $25 kg$ must be moved to keep the position of centre of mass of the system unchanged is .......... cm.

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answer is 8.

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Detailed Solution

$Δ x_{G} = \frac{m_{1} Δ x_{1} + m_{2} Δ x_{2}}{m_{1} + m_{2}} 0 = \frac{40 \times 5 + 25 (Δ x_{2})}{65} Δ x_{2} = - 8 c m$
Block of mass 25 kg will move towards 40 kg.

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