Answer:
d)[tex]4.2\times 10^{42}[/tex]
Explanation:
We are given that
[tex]M_e=9.11\times 10^{-31} kg[/tex]
[tex]K_e=8.99\times 10^9Nm^2/C^2[/tex]
[tex]G=6.67\times 10^{-11} Nm^2/kg^2[/tex]
[tex]1 e-=1.6\times 10^{-9} C[/tex]
[tex]r=1 cm=\frac{1}{100}=0.01m[/tex]
By using 100cm=1 m
Electric force=[tex]F_e=\frac{Kq_1q_2}{r^2}[/tex]
Using the formula
[tex]F_e=\frac{8.99\times 10^9\times (1.6\times 10^{-19})^2}{(0.01)^2}[/tex]
[tex]F_e=2.3\times 10^{-24} N[/tex]
Gravitational force,[tex]F_g=\frac{Gm_1m_2}{r^2}[/tex]
Using the formula
[tex]F_g=\frac{6.67\times 10^{-11}\times (9.11\times 10^{-31})^2}{(0.01)^2}[/tex]
[tex]F_g=5.54\times 10^{-67} N[/tex]
[tex]\frac{F_e}{F_g}=\frac{2.3\times 10^{-24}}{5.54\times 10^{-67}}[/tex]
[tex]\frac{F_e}{F_g}=4.2\times 10^{42}[/tex]
Option d is true.
The ratio of the electric force to the gravitational force between them is d. 4.2 × 10⁴²
The electric force between the two electrons according to Coulomb's law is F = ke²/r² where
Also, the gravitational force between the electrons according to Newton's law of gravitation is f = GMe²/r² where
Since we want to find the ratio between the electric force and the gravitational force, we have F/f = ke²/r² ÷ GMe²/r²
= ke²/GMe²
Substituting the values of the variables into the equation, we have
ke²/GMe² = 8.99 × 10⁹ Nm²/C² × (1.6 × 10⁻¹⁹ C)²/[6.67 × 10⁻¹¹ Nm²/kg² × (9.11 × 10⁻³¹ kg)²]
= 8.99 × 10⁹ Nm²/C² × 2.56 × 10⁻³⁸ C²/[6.67 × 10⁻¹¹ Nm²/kg² × 82.9921 × 10⁻⁶² kg²]
= 23.0144 × 10⁻²⁹ Nm²/553.557307 × 10⁻⁷³ Nm²
= 0.0416 × 10⁴⁴
= 4.16 × 10⁴²
≅ 4.2 × 10⁴²
So, the ratio of the electric force to the gravitational force between them is d. 4.2 × 10⁴².
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