Question:
Acceleration due to gravity at earth's surface is $g \,ms ^{-2}$. Find the effective value of gravity at a height of $32\, km$ from sea level $:\left(R_{e}=6400 \,km \right)$
Acceleration due to gravity at earth's surface is $g \,ms ^{-2}$. Find the effective value of gravity at a height of $32\, km$ from sea level $:\left(R_{e}=6400 \,km \right)$
Updated On: Jul 27, 2022
- $0.5\,g\,ms^{-2}$
- $0.99\,g\,ms^{-2}$
- $1.01\,g\,ms^{-2}$
- $0.90\,g\,ms^{-2}$
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The Correct Option is B
Solution and Explanation
For height $h$ above the earth's surface
$g'=g\left(1-\frac{2 h}{R_{e}}\right)=g\left(1-\frac{64}{6400}\right) $
$\left(\because R_{e}=6400 \,km \right) $
$=g(1-0.01) $
$= 0.99\, g\, ms ^{-2}$
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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].