Consider a pair of planets for which the distance between them is decreased by a factor of 4. How many times does the force between them increase? F (after)/ F(before)= ???? Som…

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asked Apr 1, 2024 195k views

1 Answer

Asad Ali Choudhry · Answer 1 · 2024-04-04T15:15:05+0000

Answer: the force will increase 16 times

Step-by-step explanation:

as the equation of the force is written, it's denominator is the distance squared

$f = G\frac{m_(1).{m_(2)}}{r^(2) }$

so the distance is reduced by a factor of 4 ,the equation becomes
$f = G\frac{m_(1).{m_(2)} }{{[r/4]}^(2) }$

now as the distance r is divided by 4 the complete equation is multiplied by 16.