Question:
The value of g on earth's surface is $980\,cms^{-2}$. The value at a height of 64 km from surface of earth is
The value of g on earth's surface is $980\,cms^{-2}$. The value at a height of 64 km from surface of earth is
Updated On: Jul 7, 2022
- $960.4\, cm s^{-2}$
- $984.9 \,cm s^{-2}$
- $982.45 \,cm s^{-2}$
- $977.55\, cm s^{-2}$
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The Correct Option is A
Solution and Explanation
Using $g_h = g \frac{R^2}{(R + h)^2}$, we get $g_h = 980 \left(\frac{6400}{6400 + 64} \right)^2$ = 960 cm $s^{-2}$
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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].