Question

If the gravitational force between two bodies if f. If the mass of each body is doubled and the distance between them is halved, then the force between them will be

Answer 1

formula is intially F=GMm/r^2        (1)   now each mass is doubled and distance between them is done half so      the new force is F'=G2M2m/(r/2)^2   (2)     now divide(1) by (2) you willget  F'=16F this us the ans.

Answer 2

The mass of each body is doubled and the distance between them is halved, then the force between them will be 16 time the initial force.

Explanation:

The gravitational force between two bodies is given by :

$F=G\dfrac{m_1m_2}{d^2}$

G is the gravitational constant

$m_1\ and\ m_2$ are masses

d is the distance between masses

If mass of each body is doubled and the distance between them is halved such that,

$m_1'=m_2'=2m$

$d'=\dfrac{d}{2}$

New gravitational force is given by :

$F'=G\dfrac{m_1'm_2'}{d^2}$

$F'=G\dfrac{(2m)^2}{(d/2)^2}$

$F'=16\times G\dfrac{m_1m_2}{r^2}$

$F'=16\times F$

So, the mass of each body is doubled and the distance between them is halved, then the force between them will be 16 time the initial force.

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