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A body of mass \( 5 k g \) is cut into two parts of masses (a) \( \frac{m}{4} ; \frac{3 m}{4} \) (b) \( \frac{m}{7} ; \frac{5 m}{7} \) (c) \( \frac{\boldsymbol{m}}{2} ; \frac{\boldsymbol{m}}{\boldsymbol{2}} \) (d) \( \frac{\boldsymbol{m}}{\mathbf{5}} ; \frac{\boldsymbol{4} \boldsymbol{m}}{\mathbf{5}} . \) When these two pieces are kept apart by certain distance; In which case the gravitational force acting is maximum?

1. In case a
2. In case \( c \)
3. In case d
4. In case b

Correct answer: In case d

Solution

For a fixed total mass, gravitational force between two pieces at the same separation is proportional to the product of their masses. The product is largest when the masses are closest to equal, which happens in case d among the given options.

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