Question

Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the separation of the balls, what will now be the magnitude of the attractive force on each one?A) 16F
B) 8F
C) 4F
D) F
E) F/4

Answer 1

Answer:

D) F

Explanation:

Let m and M be the mass of the balls A and B respectively and r be the distance between the two balls. The magnitude of attractive gravitational force experienced by the balls due to each other is given by the relation :

$F=\frac{GMm}{r^{2} }$      ......(1)

Now, if the masses of both the balls gets doubled as well as there separation distance also gets doubled, then let F₁ be the new gravitational force acting on them.

Since, New mass of ball A = 2M

           New mass of ball b = 2m

Distance between the two balls = 2r

Substitute these values in equation (1).

$F_{1} =\frac{G(2M)(2m)}{(2r)^{2} }$

$F_{1} =\frac{4GMm}{4r^{2} }=\frac{GMm}{r^{2} }$

Using equation (1) in the above equation.

F₁ = F