The Ratio of gravity field due to the earth at high hP and hQ from the earth's surface is \(\frac{g_{P}}{g_{Q}}=\frac{36}{25}.\) If \(h_P=\frac{R}{2}\), then the value of hQ will be
The Ratio of gravity field due to the earth at high hP and hQ from the earth's surface is \(\frac{g_{P}}{g_{Q}}=\frac{36}{25}.\) If \(h_P=\frac{R}{2}\), then the value of hQ will be
- \(\frac{3R}{4}\)
- \(\frac{3R}{5}\)
- \(\frac{4R}{5}\)
- \(\frac{5R}{6}\)
The Correct Option is C
Solution and Explanation
\(\frac{g_P}{g_Q}=\frac{\frac{GM}{r_p^2}}{\frac{GM}{r_q^2}}=\frac{36}{25}\)
\(\frac{r_Q}{r_P}=\frac{6}{5}\) \(\Rightarrow\) \(r_Q=(\frac{6}{5})(\frac{3R}{2})=\frac{9R}{5}\)
\(h_Q=\frac{9R}{5}-R=\frac{4R}{5}\)
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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].