Question:
At what height above the surface of earth the value of acceleration due to gravity would be half of its value on the surface of earth? (Radius of the earth is 6400 km)
At what height above the surface of earth the value of acceleration due to gravity would be half of its value on the surface of earth? (Radius of the earth is 6400 km)
Updated On: Jul 6, 2022
- 2561 km
- 2650 km
- 3200 km
- 9800 km
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The Correct Option is B
Solution and Explanation
The ratio
$\frac{g'}{g}=\frac{R^2}{(R+h)^2}=\frac{1}{2}$
or $R+h=\sqrt{2R}$
or $h=(\sqrt2-1)R$
or $h=(0.414)\times6400.$
$\Rightarrow$ h=2650 km
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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].