The earth is assumed to be a sphere of radius R. A platform is arranged at a height R from the surface of the earth. The escape velocity of a body from this platform is fve, where ve is its escape velocity from the surface of the earth. The value of f is :
- 2
- \(\frac{1}{\sqrt 2}\)
- \(\frac{1}{3}\)
- 4
The Correct Option is B
Solution and Explanation
Here, v = \(\sqrt{\frac{2GM}{R}}\) and kv=\(\sqrt{\frac{2GM}{R+R}}\)
Solving k =\(\frac{1}{\sqrt 2}\)
Therefore, the correct option is (B): \(\frac{1}{\sqrt 2}\)
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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].