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Universal Law of Gravitation

The gravitati...

Question

The gravitational force of attraction between two objects is x. Keeping the masses of the objects unchanged, if the distance between the objects is halved, then the magnitude of gravitational force between them will become :

(a) x/4
(b) x/2
(c) 2x
(d) 4x

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Solution

(d) 4x
G = x
m₁ and m₂ are constant
Since, r is reduced to half, let, r/ = r/2
Gravitation force, F = G × m₁ × m₂/r² = x
When r is reduced to half the force becomes, F/ = G × m₁ × m₂/(r/)²
= G × m₁ × m₂ /(r/2)²
= 4x

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