Question

Consider an electron moving with relativistic speed v and momentum of magnitude p. If the speed of the electron is doubled, the resulting relativistic momentum of the electron will be:a) equal to 2pb) less than 2pc) greater than 2pPlease explain why.

Answer 1

Answer:

option (b)

Explanation:

initial speed = v

initial momentum = p

final speed = 2v

final momentum = p'

The formula for relativistic momentum is given by

$p = \frac{mv}{\sqrt{1-\frac{v^{2}}{c^{2}}}}$     .... (1)

The new momentum is given by

$p' = \frac{m\times 2v}{\sqrt{1-\frac{4v^{2}}{c^{2}}}}$     .... (2)

By comparison, p' < 2p.

Thus, the option is (b) .