A thought experiment on gravitation

A thought experiment on gravitation....

Let us suppose we have a very large planet X which is assumed to have some acceleration 'a'. Suppose we keep on digging a well and afterwards we drop a small mass 'm' then due to the force there will be an acceleration. As acceleration is change in velocity with change in time hence the velocity keeps on increasing as the ball falls further down then is it possible that the mass 'm' will acquire the velocity of light 3x10^8 m/s?? If not then why (the body is accelerating)? If it will then what happens next, as in can it go any faster than light??

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Dale
Mentor

Regardless of how large the planet is its mass is finite. Therefore the difference in gravitational potential energy between the surface and the center is finite. So the object will gain a finite amount of KE. Any finite KE will have a veocity less than c.

mfb
Mentor

More general, a constant force in your lab system does not give a constant acceleration (this is just a nonrelativistic approximation for low velocity) - as soon as the object gets close to the speed of light, you need more and more force and energy to increase its velocity. You can get as close to the speed of light as you want, neglecting technical issues, but you can never reach it.