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2 years ago

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Two small balls, A and B, attract each other gravitationally with a force of magnitude F. If we now double both masses and the s

eparation 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

1 answer:

Nimfa-mama [501]2 years ago

4 0

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

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