Q. For a body moving with relativistic speed, if the velocity is doubled, then
A) Its linear momentum is doubled
B) Its linear momentum will be less than double
C) Its linear momentum will be more than double
D) Its linear momentum remains unchanged
Explanation
(a) From Einstein’s theorem
Relativistic momentum $= \frac{m_{0}v}{\sqrt{1 - v^{2}/c^{2}}}$
Putting $v = 2v$
We get $p = \ \frac{m_{0}(2v)}{\sqrt{1 - {(2v}^{2})/c^{2}}} = 2\left( \frac{m_{0}v}{\sqrt{1 - {4v}^{2}/c^{2}}} \right)$
So, the momentum becomes more than the double.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.