# An object with a nonzero rest mass moving at the speed of light would have a. infinite volume. ...

## Question:

An object with a nonzero rest mass moving at the speed of light would have

a. infinite volume.

b. time pass at an infinitely fast rate.

c. infinite apparent mass.

d. no momentum.

## The Special Theory of Relativity and the Lorentz Factor:

The special theory of relativity was fully developed by Albert Einstein at the beginning of the 20th century, based on the research of scientists in geometrical optics, electromagnetism and experimental evidence on the finite and constant speed of light in vacuum, regardless of inertial reference frame. The theory of special relativity predicts the dilation in time, contraction of dimensions, among several other phenomena.

## Answer and Explanation:

From the equations of special relativity, it can be found that to correctly calculate the momentum, when a change in inertial reference frame is performed, it changes as:

{eq}\vec{p}=m\vec{v},\qquad m=\frac{m_{0}}{\sqrt{1-\frac{\vec{v}^{2}}{c^{2}}}}, {/eq}

where:

- {eq}m_{0} {/eq} is the rest mass.

- {eq}\vec{v} {/eq} is the velocity such that {eq}\left|\vec{v}\right|<c; {/eq} so that {eq}c {/eq} is the speed of light in vacuum.

Thus, as {eq}\left|\vec{v}\right| {/eq} approaches {eq}c {/eq}, the mass grows. When {eq}\left|\vec{v}\right| {/eq} gets to {eq}c {/eq}, the measured mass goes to infinity; this will never happen, of course, but in principle it would. Thus, the answer is **c.** .

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