Question:
The escape velocity of a body depends upon its mass as
The escape velocity of a body depends upon its mass as
Updated On: Jul 7, 2022
- $m^0$
- $m^1$
- $m^2$
- $m^3$
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The Correct Option is A
Solution and Explanation
Escape speed of a body from Earth's surface is given by: $v _{\min }=\sqrt{2 gR }$
As we can see from the above equation, there is no 'mass' term. Implies it can be written as $m ^{0}$.
So, the escape speed of a body is independent of its mass.
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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].