(a) A proton is moving at a speed much less than the speed of light. It has kinetic energy `K_1` and momentum `p_1`. If the momentum of the proton is doubled, so `p_2 = 2 p_1`, how is its new kinetic energy `K_2` related to `K-1`?
(b)A photon with energy `E_1` has momentum `p_1` . if another photon has momentum `p_2` that is twice `p_1`, how is the energy `E_2` of the second photon related to `E_1`?

Answer

A, B, D

Explanation

(a) `K = (P)^2/(2m) or K prop p^2`
if momentum is doubled, kinetic energy
becomes four times.
(b) `P = (E )/(c ) or E prop P`
If p is doubled, E will also become two times.