Working of force of gravitation on the objects moving at the speed comparable to the speed of light If two clamped objects of mass m starts moving at the speed comparable to the speed of light.Will the gravitational force between them increase?
$$
m=\frac{m_0}{\sqrt{1-\frac{v^2}{c^2}}}
$$
This formula says that the mass of a body will increase as it's speed increases.
$$
F_g=\frac{G\,m_1\,m_2}{r^2}
$$
If I take mass of each (clamped) body as m and a if I draw a graph by substituting the masses at the high velocity into the Newton's laws of gravitation, 
I get a graph like this
:

 A: The answer is no, it won't.
Rather than give some detailed bit of maths to explain why this is, I'll give a more general argument which you can use to answer not only this question but any similar question.
The argument is this: consider yourself as an ant sitting on one of the masses (an ant so you don't perturb the forces very much).  You have in your hand (claw?) a bit of paper on which are written two conflicting statements:


*

*'your speed is $0$';

*'your speed is $0.97c$'.


You now need to tell me which of these statements is true: what experiment can you do to answer this question?
Well the answer is, of course, that there is no experiment that you can do which will distinguish between these two statements.  And, since that is the case, there can be no difference in the force experienced by the masses, from your point of view.
This sounds like a trite answer, but it's not: this trick of noticing that there is no possible observational way of distinguishing between two situations which are claimed to be different, and so they are not different is absolutely critical to understanding relativity, and is a very powerful tool.
