Question

The rest mass of a body is ${{m}_{0}}$. If it moves with a velocity of 0.6 m/s, then its relativistic mass is m, then:
A). $m<{{m}_{0}}$
B). $m={{m}_{0}}$
C). $m>{{m}_{0}}$
D). None of these

Answer 1

Hint: In order to answer this question, we have to develop a formula establishing a relationship between the rest mass of a body and the relativistic mass of a body. By rest mass of a body we mean, the mass of the body which is to be measured when the body is at rest with respect to that of an observer. This is considered to be an inherent property of the body. And then comes the relativistic mass. By relativistic mass we mean the mass that is assigned to a body when the body is in motion.

Complete step by step answer:
As we have already mentioned the definitions of rest mass and relativistic mass, let us know move on to the development of a relationship between them. So, here is the required formula to solve the given question:
$m=\dfrac{{{m}_{0}}}{\sqrt{1-\dfrac{{{v}^{2}}}{{{c}^{2}}}}}$
In the above mentioned formula we have m to be the relativistic mass of the body which is already given in the question.
${{m}_{0}}$is considered as the rest mass of the body, which is also given in the question.
c is the speed of light in vacuum and v is the velocity with which the body moves. The value of v for this question is mentioned as 0.6 m/s.
So let us put the values in the above mentioned formula, so we get:
$\dfrac{{{m}_{0}}}{\sqrt{1-\dfrac{{{(0.6c)}^{2}}}{{{c}^{2}}}}}$
Therefore, on solving the above expression we get,
$\dfrac{{{m}_{0}}}{\sqrt{0.64}}=\dfrac{{{m}_{0}}}{0.8}$
This shows that $m>{{m}_{0}}$. Hence, the correct answer is Option C.

Note: So from the answer we now know that, the word mass has two meanings, with respect to special relativity. The rest mass also known as invariant mass is an invariant quantity which is the same for all the observers, in all the reference frames taken into consideration. However, relativistic mass depends on the velocity of the observer.