Question

The relative strengths of gravitational, columb's and nuclear forces of protons are in the ratio (nearly)

• A. $1:1:1$
• B. $1:{10}^{36}:{10}^{38}$
• C. ${10}^{38}:{10}^{36}:1$
• D. $1:{10}^{30}:{10}^{34}$

Answer 1

The correct option is B $1:{10}^{36}:{10}^{38}$

The gravitational force between two protons separated by distance $r$ is given by,

$F_g=\frac{G{m}_p^2}{r^2}$

The electrostatic force between two protons separated by distance $r$ is given by,

$F_e=\frac{1}{4\pi {\epsilon }_0}\frac{e^2}{r^2}$

$\Rightarrow \frac{F_g}{F_e}=\frac{6.67\times {10}^{-11}(1.67\times {10}^{-27}{)}^2}{9\times {10}^9(1.6\times {10}^{-19}{)}^2}$

$\Rightarrow \frac{F_g}{F_e}\approx \frac{1}{{10}^{36}}$

Nuclear force between two protons is approximately ${10}^{38}$ times of the gravitational force.

$\Rightarrow F_g:F_e:F_n=1:{10}^{36}:{10}^{38}$

Hence, option $\left(B\right)$ is correct.