Question

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

Answer 1

Answer: (C)

From Einsteins theorem
Relativistic momentum $=\frac{m_{0} v}{\sqrt{1-v^{2} / C^{2}}}$
Putting $v=2 v$
we get $\rho=\frac{m_{0}(2 v)}{\sqrt{1-(2 v)^{2} / c^{2}}}$
$=2\left(\frac{m_{0} v}{\sqrt{1-(2 v)^{2} / c^{2}}}\right)$
So the momentum becomes more than the double.