Question:
With what velocity should a particle be projected so that its height becomes equal to radius of earth?
With what velocity should a particle be projected so that its height becomes equal to radius of earth?
Updated On: Jun 27, 2024
- $\bigg( \frac{GM}{R} \bigg) ^{1/2}$
- $\bigg( \frac{8GM}{R} \bigg) ^{1/2}$
- $\bigg( \frac{2GM}{R} \bigg) ^{1/2}$
- $\bigg( \frac{4GM}{R} \bigg) ^{1/2}$
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The Correct Option is A
Solution and Explanation
Use $ v^2 = \frac{ 2gh}{ 1+ \frac{h}{R}} $ given h = R.
$ \therefore \, \, \, \, \, v = \sqrt{gR } = \sqrt{ \frac{ GM}{ R}} $.
$ \therefore \, \, \, \, \, v = \sqrt{gR } = \sqrt{ \frac{ GM}{ R}} $.
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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].