Question:
A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u$ . The mass and the radius of the earth are, respectively, $M$ and $R. G$ is gravitational constant and $g$ is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is
A particle of mass $m$ is thrown upwards from the surface of the earth, with a velocity $u$ . The mass and the radius of the earth are, respectively, $M$ and $R. G$ is gravitational constant and $g$ is acceleration due to gravity on the surface of the earth. The minimum value of u so that the particle does not return back to earth, is
Updated On: May 5, 2024
- $ \sqrt{ \frac{ 2GM}{R^2}}$
- $ \sqrt{ \frac{ 2GM}{R}}$
- $ \sqrt{ \frac{ 2gM}{R^2}}$
- $\sqrt{2g R^2 }$
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The Correct Option is B
Solution and Explanation
$v _{\text {escape }}=\sqrt{\frac{2 GM }{ R }}$
Escape velocity from earth surface.
Escape velocity from earth surface.
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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].