Question

According to the realitivistic expression for momentum, if the speed of an object is doubled, the magnitude of its momentum.

Answer 1

P = M0 V / (1 - (V / C)^2)^1/2

Let V / C = X unless V is a close to the speed of light (10% or so)

(1 - x^2)^1/2 is a small quantity and can be ignored at small speeds.

(1 - [1 - (V/C)^2]^-1/2 = (V/C)^2 using the first terms of the binomial expansion

P2 / P1 = V2 / V1 * (X2 / X1)^2

For V<<C the effect is small and the momentum is merely doubled