Question:
A research satellite of mass 200 kg circles the earth in an orbit of average radius $\frac{3R}{2}$ where R is the radius of earth. Assuming the gravitatioaal pull on a mass of 1 kg on the earth's surface to be 10 N, the puII on the sateIlite will be
A research satellite of mass 200 kg circles the earth in an orbit of average radius $\frac{3R}{2}$ where R is the radius of earth. Assuming the gravitatioaal pull on a mass of 1 kg on the earth's surface to be 10 N, the puII on the sateIlite will be
Updated On: Apr 7, 2024
- 880 N
- 889 N
- 885 N
- 892 N
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The Correct Option is B
Solution and Explanation
On earth,$ mg= 10\, or\, 1 \times g = 10 \Rightarrow g = 10\, ms^{-2}$
Now, $\hspace10mm g' = g\frac{R^2}{r^2} = 10 \times \frac{R^2}{(3R/2)^2}=\frac{40}{9}$
Pull on satellite = m' g'
$\hspace25mm = 200 \times \frac{40}{9} = 889\, N$
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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].