Question

The gravitational force between two objects is F. If the masses of both objects
are halved without changing distance between them, then what would be the
gravitational force?
a) F/4
b) F/2
c) F
d) 2 F

Answer 1

$\bigstar$ Explaination $\bigstar$

• Given

Intially the gravitational force between the two bodies of m and M respectively is F

• To find

The new gravitational force between the two bodies if their mass have been havled

instead of changing the distance between then

• Procedure

Let the distance between the bodies be l

Let the mass of the two bodies between m and M respectively

$F = ( \frac{G\times m \times M}{l^2} )$

Let the gravitational force between the two bodies when their mass have been havled be f

$f = \frac{G \times \frac{m}{2} \times \frac{M}{2} }{l^2}$

$f = \frac{G \times \frac{Mm}{4} }{l^2}$

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

As (G x m x M)/l² = F,

Therefore,

$f = \frac{F}{4}$

$\boxed{Answer\:is\:option\:A}$