Question

$F_g$ and $F_e$ represent gravitational and electrostatic force respectively between electrons situated at a distance $0.1m.F_g/F_e$ is of the order

• A. ${10}^{-41}$
• B. ${10}^{-45}$
• C. ${10}^{40}$
• D. ${10}^{-42}$

Answer 1

The correct option is D ${10}^{-42}$

$F_y$ and $F_e$ represent gravitational and electrostatic force respectively between electrons situated at a distance $=0.1m$

let, us take the ratio

$\frac{F_e}{F_g}=\frac{\frac{1}{4\pi {ϵ}_0}\frac{q^2}{d^2}}{G\frac{m^2}{d^2}}$

$\frac{F_e}{F_g}=\frac{1}{4\pi {ϵ}_0}\times \frac{1}{G}\times \frac{q^2}{m^2}$

$\frac{F_e}{F_g}=9\times {10}^9\times \frac{1}{6.67\times {10}^{-11}}\times \frac{{(1.6\times {10}^{-19})}^2}{{(9.1\times {10}^{-31})}^2}$

$\Rightarrow \frac{F_e}{F_g}=4.17\times {10}^{42}$

or, $\frac{F_e}{F_g}$ is of the order of ${10}^{-42}$.