Question

How does force of g gravitational between two objects change when the distance between them is reduced to half

Answer 1

Well, let’s have a look at this and put it in math (this is a good skill to learn by the way, very useful for generalizing changes in state).

So we have a scenario, we’ll call it “State 1” where we have…

Fg,1=Gm1,1m2,1d21Fg,1=Gm1,1m2,1d12

This is just the equation for the magnitude of the force of gravity between two objects.

Now we’ll make an equation for state 2 where we have…

Fg,2=Gm1,2m2,2/d2,²

We were told in the problem statement that the only thing that changed is that “the distance between them was reduced to half”. That means that…

d2=12/d1

So let’s go back and make those adjustments, since everything in state two is either the same or a function of what’s in state one, we’ll take away the subscripts for the states.

Fg,2=
G m1m2/(1/2d)2
=4Gm1m2/d2=
4Fg,1,

Hey, that second part looks familiar. Yup, it’s exactly what we started with. So the force of gravitation has increased by 4 times. Granted, that’s one that you’ll learn to do in your head eventually, but this is a good thing to know how to do for when things get more complicated

Answer 2

☺ Hello mate__ ❤

◾◾here is your answer...

According to the universal law of gravitation, gravitational force (F),

F∝ 1/r^2

If distance r becomes r/2, then the gravitational force will be proportional to

F ∝ 1/ (r/2)^2 ∝ 4/r^2

Hence, if the distance is reduced to half, then the gravitational force becomes four times larger than the previous value.

I hope, this will help you.

Thank you______❤

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