Question:
If $M$ is the mass of the earth and $R$ its radius, the ratio of the gravitational acceleration and the gravitational constant is :
If $M$ is the mass of the earth and $R$ its radius, the ratio of the gravitational acceleration and the gravitational constant is :
Updated On: Apr 19, 2024
- $\frac{R^2}{M}$
- $\frac{M}{R^2}$
- $MR^{2}$
- $\frac{M}{R}$
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The Correct Option is B
Solution and Explanation
Gravitational acceleration is given by
$g=\frac{G M}{R^{2}}$
where $G=$ gravitational constant
$\therefore \, \frac{g}{G}=\frac{M}{R^{2}}$
$g=\frac{G M}{R^{2}}$
where $G=$ gravitational constant
$\therefore \, \frac{g}{G}=\frac{M}{R^{2}}$
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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].