Question:
If $F_g$ and $F_e$ are gravitational and electrostatic forces between two electrons at a distance 0.1 m then $F_g/F_e$ is in the order of
If $F_g$ and $F_e$ are gravitational and electrostatic forces between two electrons at a distance 0.1 m then $F_g/F_e$ is in the order of
Updated On: Jun 21, 2022
- $10^{43}$
- $10^{-43}$
- $10^{35}$
- $10^{-35}$
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The Correct Option is A
Solution and Explanation
$\frac{ F _{ e }}{ F _{ g }}=\frac{ q _{1} q _{2}}{4 \pi \epsilon_{0} r ^{2}} / \frac{ Gm _{1} m _{2}}{ r ^{2}}$
$\frac{ F _{ e }}{ F _{ g }}=\frac{ q ^{2}}{4 \pi \epsilon_{0} Gm ^{2}}$
$\frac{ F _{ e }}{ F _{ g }}=\frac{9 \times 10^{9} \times\left(1.6 \times 10^{-19}\right)^{2}}{6.67 \times 10^{-11} \times\left(9.1 \times 10^{-31}\right)^{2}}=0.417 \times 10^{43}$
$\frac{ F _{ e }}{ F _{ g }}=\frac{ q ^{2}}{4 \pi \epsilon_{0} Gm ^{2}}$
$\frac{ F _{ e }}{ F _{ g }}=\frac{9 \times 10^{9} \times\left(1.6 \times 10^{-19}\right)^{2}}{6.67 \times 10^{-11} \times\left(9.1 \times 10^{-31}\right)^{2}}=0.417 \times 10^{43}$
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Concepts Used:
Gravitation
In mechanics, the universal force of attraction acting between all matter is known as Gravity, also called gravitation, . It is the weakest known force in nature.
Newton’s Law of Gravitation
According to Newton’s law of gravitation, “Every particle in the universe attracts every other particle with a force whose magnitude is,
- F ∝ (M1M2) . . . . (1)
- (F ∝ 1/r2) . . . . (2)
On combining equations (1) and (2) we get,
F ∝ M1M2/r2
F = G × [M1M2]/r2 . . . . (7)
Or, f(r) = GM1M2/r2
The dimension formula of G is [M-1L3T-2].