Question:
A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased
A geostationary satellite is revolving around the earth. To make it escape from gravitational field of earth, its velocity must be increased
Updated On: Jun 6, 2024
- $ 100\% $
- $ 41.4\% $
- $ 50\% $
- $ 59.6\% $
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The Correct Option is B
Solution and Explanation
Orbital velocit $ v_o=\sqrt{gR_e} $
Escape velocity $ v_e=\sqrt{2gR_e} $
where $ R_e $ is radius of earth.
$\%$ increase $ =\frac{v_e-v_o}{v_o}\times100 $
$\%$ increase $ =\frac{\sqrt{2gR_e}-\sqrt{gR_e}}{\sqrt{gR_e}}\times100 $
$ =(\sqrt2-1)\times100 $
$ =(1.414-1)\times100=41.4\% $
Escape velocity $ v_e=\sqrt{2gR_e} $
where $ R_e $ is radius of earth.
$\%$ increase $ =\frac{v_e-v_o}{v_o}\times100 $
$\%$ increase $ =\frac{\sqrt{2gR_e}-\sqrt{gR_e}}{\sqrt{gR_e}}\times100 $
$ =(\sqrt2-1)\times100 $
$ =(1.414-1)\times100=41.4\% $
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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].