Answer : The correct option is, (B) [tex]1.3\times 10^{-18}kg.m/s[/tex]
Explanation : Given,
Mass of proton = [tex]1.673\times 10^{-27}kg[/tex]
Speed of proton = 0.93 c
Formula used for relativistic momentum of the proton is:
[tex]p=\frac{m_ov}{\sqrt{1-\frac{v^2}{c^2}}}[/tex]
where,
p = relativistic momentum of the proton
[tex]m_o[/tex] = mass of proton
v = speed of proton
c = speed of light = [tex]3\times 10^8m/s[/tex]
Now put all the given values in the above formula, we get:
[tex]p=\frac{(1.673\times 10^{-27}kg)\times (0.93c)}{\sqrt{1-\frac{(0.93c)^2}{c^2}}}[/tex]
[tex]p=\frac{(1.55589\times 10^{-27}c)}{0.367}[/tex]
[tex]p=\frac{(1.55589\times 10^{-27})\times (3\times 10^8)}{0.367}[/tex]
[tex]p=1.272\times 10^{-18}kg.m/s\approx 1.3\times 10^{-18}kg.m/s[/tex]
Therefore, the relativistic momentum of the proton is, [tex]1.3\times 10^{-18}kg.m/s[/tex]
