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)

its linear momentum will be more than double

From Einstein's theorem
Relativistic momentum $=\frac{m_{0}v}{\sqrt{1-v^2/c^2}}$
Putting $v=2v$
we get $p=\frac{m_0\left(2v\right)}{\sqrt{1-(2v{)}^2/c^2}}$
$=2\left(\frac{m_{0}v}{\sqrt{1-(2v{)}^2/c^2}}\right)$.

Thus if the velocity is doubled, the relativistic mass also increases and hence the linear momentum will be more than double.