A) (Charge on electron \[=1.6\times {{10}^{-19}}C\] mass of electron \[=9.1\times {{10}^{-31}}\text{kg,}\] mass of proton\[=1.6\times {{10}^{-27}}kg\],\[G=6.7\times {{10}^{-11}}\text{N}{{\text{m}}^{2}}\text{/kg)}\] \[2.36\times {{10}^{39}}\]
B) \[2.36\times {{10}^{40}}\]
C) \[2.34\times {{10}^{41}}\]
D) \[2.34\times {{10}^{42}}\]
Correct Answer: A
Solution :
Gravitational force \[F=\frac{G{{M}_{1}}{{M}_{2}}}{{{r}^{2}}}\] \[{{F}_{G}}=\frac{6.7\times {{10}^{-11}}\times 9.1\times {{10}^{-31}}\times 1.6\times {{10}^{-27}}}{{{(5\times {{10}^{-11}})}^{2}}}\] \[=3.9\times {{10}^{-47}}N\] Electrostatic force \[{{F}_{E}}=\frac{1}{4\pi {{\varepsilon }_{0}}}\frac{{{q}_{1}}{{q}_{2}}}{{{r}^{2}}}\] \[{{F}_{e}}=\frac{9\times {{10}^{9}}\times 1.6\times {{10}^{-19}}\times 1.6\times {{10}^{-19}}}{{{(5\times {{10}^{-11}})}^{2}}}\] \[=9.22\times {{10}^{-8}}N\] \[\therefore \frac{\text{Electrostatic}\,\text{force}}{\text{Gravitational}\,\text{force}}=\frac{{{F}_{E}}}{{{F}_{G}}}\] \[=\frac{9.22\times {{10}^{-8}}}{3.9\times {{10}^{-47}}}\] \[=2.36\times {{10}^{39}}\]
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