Question

proton is accelerated to a speed of 0.93c, what is the 1. A proton has a mass of 1.673 x 10-27 kg. If the proton is accelerated to a speed magnitude of the relativistic momentum of the proton? A. 6.2 x 10-17 kg. m/s B. 1.3 x 10-18 kg. m/s C. 4.7 x 10-19 kg. m/s D. 5.9 x 10-24 kg. m/s E. 1.8 * 10-18 kg . m/s

Answer 1

Answer : The correct option is, (B) $1.3\times 10^{-18}kg.m/s$

Explanation : Given,

Mass of proton = $1.673\times 10^{-27}kg$

Speed of proton = 0.93 c

Formula used for relativistic momentum of the proton is:

$p=\frac{m_ov}{\sqrt{1-\frac{v^2}{c^2}}}$

where,

p = relativistic momentum of the proton

$m_o$ = mass of proton

v = speed of proton

c = speed of light = $3\times 10^8m/s$

Now put all the given values in the above formula, we get:

$p=\frac{(1.673\times 10^{-27}kg)\times (0.93c)}{\sqrt{1-\frac{(0.93c)^2}{c^2}}}$

$p=\frac{(1.55589\times 10^{-27}c)}{0.367}$

$p=\frac{(1.55589\times 10^{-27})\times (3\times 10^8)}{0.367}$

$p=1.272\times 10^{-18}kg.m/s\approx 1.3\times 10^{-18}kg.m/s$

Therefore, the relativistic momentum of the proton is, $1.3\times 10^{-18}kg.m/s$