Question

if the masses of two bodies are quadrupoled and the distance between them is doubled the force between them will

Answer 1

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Then force between them will be 4 times.

${\huge{\boxed{\mathcal{\red{Explanation}}}}}$

According to universal law of gravitation : the force of gravitation between two bodies is directly proportional to product of their masses and inversely proportional to square of distance between them. This law can be represented mathematically with the help of equation :

$f = G \frac{Mm}{ {d}^{2} }$

In this equation :

• G = universal gravitational constant
• M = mass of first body
• m = mass of second body
• d = distance between bodies.
• f = force of gravitation.

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Now according to the given condition :

In this case :

M = 4M

m = 4m

d = 2d.

Thus in thus case force of gravitation will be :

$f = G \frac{4m \times 4m}{ {2d}^{2} }$

$f = 4(G \frac{mm}{ {d}^{2} } )$

Thus after adding both equations we can conclude that the force will increase by 4 times.

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BY SCIVIBHANSHU

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