Question

prove that f=g× m¹×m²/d²​

Answer 1

Answer:

Explanation:

Here is the derivation of force exerted by gravitation on any object.

Answer 2

Answer:

Yes, it's true that the greater the distance between two objects with mass, the less gravitational force each will exert on the other. It gets a little more complicated in some cases - I'm thinking of the variation of the Earth's gravity - but that's the general rule.

I'm assuming that by "explain W=mgW=mg", you're asking what the implications of this varying force are on weight. The answer is that weight varies with distance too.

How is this possible? Well, take a look at this formula:

g(r)=−GM(r)r2g(r)=−GM(r)r2

It's an approximation (you can find more info about its assumptions here) for gravitational acceleration due to a spherical body such as Earth. Notice that gg varies with distance rr... and since WW is a function of gg, it must vary as well!

You might have been told that g≈9.8m/sg≈9.8m/s, but this is really just the value at the Earth's surface. If you get significantly closer or further away from Earth, you'll find it varies.

Edit: The question originally read "the greater the distance, the more force will act...". Original answer below:

I think you've misread the equation! Let me format it a little more nicely:

F=Gm1m2d2F=Gm1m2d2

We can see that as dd increases, so does the bottom of the fraction, so the total force FF decreases... for the same reason that 12>1412>14!