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Question:
The gravitational field strength at the surface of a certain planet is $g$. Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?
The gravitational field strength at the surface of a certain planet is $g$. Which of the following is the gravitational field strength at the surface of a planet with twice the radius and twice the mass?
Updated On: May 12, 2024
- $g/2$
- $g$
- $2g$
- $4g$
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The Correct Option is A
Solution and Explanation
For a given planet, $g = \frac{GM}{R^2}$
Gravitational field strength at the surface of another planet, $g' = \frac{GM'}{R'^2}$
Here, $M' = 2M , R' = 2R$
$\therefore \:\:\: g' = \frac{G(1M)}{(2R)^2} = \frac{g}{2}$
Gravitational field strength at the surface of another planet, $g' = \frac{GM'}{R'^2}$
Here, $M' = 2M , R' = 2R$
$\therefore \:\:\: g' = \frac{G(1M)}{(2R)^2} = \frac{g}{2}$
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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].
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