Question

The gravitational force between two spheres in outer space is 1000 n. how large would this force be if the mass of each sphere were doubled and the distance between them were doubled?

Answer 1

The force will remain same if the mass of each sphere is doubled and the distance between them is doubled as well.

The force of gravitation between two spheres is given by

$f=\frac{G m1 m2}{r^{2}}$

m1= mass of first object

m2= mass of second object

r= distance between the masses

Now if each mass is doubled and the distance r is doubled as well

$F'= \frac{G (2m1)(2m2)}{(2r)^{2}}$

$F'= \frac{4 G m1 m2}{4r^{2}}$

F'=$\frac{G m1 m2 }{r^{2}}$

so F'= F

so the force remains same and is equal to 1000 N.