Question

If the speed of a particle moving at a relativistic speed is doubled, its linear momentum will

• A. become double
• B. become more than double
• C. remain equal
• D. become less than double

Answer 1

The correct option is B become more than double

Let the speed of the particle initially be $v$.

Thus initial linear momentum $P_i=\frac{m_{o}v}{\sqrt{1-\frac{v^2}{c^2}}}$ where $m_o$ is the rest mass of particle

Now the speed of the particle is doubled i.e $v^{\prime }=2v$

$\therefore$ New linear momentum $P_f=\frac{m{v}^{\prime }}{\sqrt{1-\frac{(v^{\prime }{)}^2}{c^2}}}=$ $\frac{m_o\left(2v\right)}{\sqrt{1-\frac{(2v{)}^2}{c^2}}}>2P_i$

Hence option B is correct.