Inertia is directly proportional to mass but what happens when something travel to speed near to light. Its relativistic mass tends to infinity but that is false mass so I want to know if inertia is applied to relativistic mass. Because if we infinite the mass then the inertia would also be infinite then it will never reach speed of light.
[Physics] Inertia on relativistic mass when particle is near speed of light
inertiamassspecial-relativityspeed-of-light
Related Solutions
The mass (the true mass which physicists actually deal with when they calculate something concerning relativistic particles) does not change with velocity. The mass (the true mass!) is an intrinsic property of a body, and it does not depends on the observer's frame of reference. I strongly suggest to read this popular article by Lev Okun, where he calls the concept of relativistic mass a "pedagogical virus".
What actually changes at relativistic speeds is the dynamical law that relates momentum and energy depend with the velocity (which was already written). Let me put it this way: trying to ascribe the modification of the dynamical law to a changing mass is the same as trying to explain non-Euclidean geometry by redefining $\pi$!
Why this law changes is the correct question, and it is discussed in the answers here.
I've heard that a spacecraft could never exceed the speed of light because it's (relativistic) mass quickly approaches infinity and therefore there could never create a big enough rocket to propel it faster and faster.
In fact, the spacecraft could never even reach, much less exceed the speed of light.
I think that you'll agree that the spacecraft, no matter what speed it may have relative to some other object, is at rest with respect to itself.
Think carefully about that! The spacecraft (or any material object) is not moving with respect to itself.
This seems so intuitive, so unquestionably true that you might think that there is no reason to even mention it.
But, according to Special Relativity, something that moves with speed c (the speed of light in vacuum) relative to some other object, moves with speed c relative to any object (c is an invariant speed).
In other words, if it were the case that the spacecraft could obtain the speed of light, it would be moving at the speed of light with respect to itself.
This is so plainly incomprehensible that it is, in fact, a relief to know that the spacecraft can never attain the speed of c.
More precisely, according to the Lorentz transformations, there is no frame of reference that moves with speed c relative to another frame of reference.
More generally, this fact "shows up" as nonsense statements like "the mass is infinite at the speed of light" or "infinite force is required to get to the speed of light".
There's no such thing as infinite mass or infinite force which is to say, you can't get to c from here.
Best Answer
By inertia I assume you mean momentum. The momentum is related to the energy of the object by:
$$ E^2 = p^2c^2 + m^2c^4 $$
and to the velocity by:
$$ p = \frac{mv}{\sqrt{1 - \frac{v^2}{c^2}}} $$
The momentum does indeed tend to infinity as $v \rightarrow c$, but note that it will never reach an infinite value because no massive object can travel at the speed of light so $v$ never reaches $c$.