Question

The distance between two particles was reduced from 6 m to 2 m. The force of gravity between these particles will thus be increased by a factor of is
(a) 3
(b) 4
(c) 9
(d) 36​

Answer 1

Given:

The distance between two particles was reduced from 6 m to 2 m.

To find:

Factor by which gravitational force changes?

Calculation:

Initial Gravitation Force is :

$F_{i} = \dfrac{G {m}^{2} }{ {6}^{2} }$

$\implies F_{i} = \dfrac{G {m}^{2} }{36}$

Final Gravitational Force:

$F_{f} = \dfrac{G {m}^{2} }{ {2}^{2} }$

$\implies F_{f} = \dfrac{G {m}^{2} }{4}$

Now, dividing the equations:

$\implies \: \dfrac{F_{f}}{F_{i}} = \dfrac{36}{4}$

$\implies \: \dfrac{F_{f}}{F_{i}} = 9$

$\implies \: F_{f} = 9 \times F_{i}$

So, final force changes by factor of 9.

Answer 2

Explanation:

9 is the answer

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