Question

What happens to the gravitational force between two objects when the distance between them is :
(i) doubled?
(ii) halved?

Answer 1

Answer:

1) doubled-the force is doubled(increased)

2)halfed-the force is halfed(decreased)

Answer 2

Answer: i) quartered ii) quadrupled

Explanation:

Fg = $\frac{Gm_{1}m_{2}}{d^{2} }$

where

Fg = Force due to gravity/gravitational force

G = Universal Gravitational Constant = 6.67 x 10^-11 $\frac{Nm^{2}}{kg^{2}}$

$m_{1}$ = mass of object 1

$m_{2}$ = mass of object 2

d = distance between the two objects.

i) Applying the formula for when distance is doubled (2x)

=> Fg = $\frac{Gm_{1}m_{2}}{(2d)^{2} }$

        => $\frac{Gm_{1}m_{2}}{2^{2}d^{2} }$

        => $\frac{Gm_{1}m_{2}}{4d^{2} }$  

        => $\frac{1}{4}$ x $\frac{Gm_{1}m_{2}}{d^{2} }$  = $\frac{1}{4}$ x Fg ---> quartered

ii) Applying the formula for when distance is halved ($\frac{1}{2}$x)

=> Fg = $\frac{Gm_{1}m_{2}}{(\frac{1}{2}d)^{2} }$

        => $\frac{Gm_{1}m_{2}}{\frac{1}{2}^{2}d^{2} }$

        => $\frac{Gm_{1}m_{2}}{\frac{1}{4}d^{2} }$  

        => 4 x $\frac{Gm_{1}m_{2}}{d^{2} }$  = 4 x Fg ---> quadrupled