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How does the force of gravitation between two objects change when the distance between them is reduced to half? 

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According to the universal law of gravitation, gravitational force (F) acting between two objects is inversely proportional to the square of the distance (r) between them, i.e., 

f ∝ 1 / r 

If distance r becomes r/2, then the gravitational force will be proportional to 

1 / ( r/2 ) 2 = 4 / r 

Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.

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