Question:
A research satellite of mass $200\, kg$ circle the earth in an orbit of average radius $ \frac{3R}{2}, $ where is the radius of the earth. Assuming the gravitational pull on a mass of $1\, kg$ on the earths surface to. be $10\, N$, the pull on the satellite will be
A research satellite of mass $200\, kg$ circle the earth in an orbit of average radius $ \frac{3R}{2}, $ where is the radius of the earth. Assuming the gravitational pull on a mass of $1\, kg$ on the earths surface to. be $10\, N$, the pull on the satellite will be
Updated On: Jul 12, 2022
- 880 N
- 889 N
- 890 N
- 892 N
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The Correct Option is B
Solution and Explanation
Given,
$10=\frac{G \times 6 \times 10^{24} \times 1}{\left(6.4 \times 10^{6}\right)^{2}}$
$\Rightarrow G=6.82 \times 10^{-11} Nm ^{2} / kg ^{2}$
Therefore,
$F_{\text {satellite}}=\frac{6.82 \times 10^{-11} \times 6 \times 10^{24} \times 200}{\left(\frac{3 \times 6.4 \times 10^{6}}{2}\right)^{2}}$
$=889\, N$
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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].