A mass �m� on the surface of the Earth is shifted to a target equal to the radius of the Earth. If �R� is the radius and �M� is the mass of the Earth, then work done in this process is
- $\frac{mgR}{2}$
- $mgR$
- $2 \, mgR$
- $\frac{mgR}{4}$
The Correct Option is A
Solution and Explanation
$U_T = \frac{- GMm}{2R}$
$W = U_T - U_E = \frac{-GMm}{2R} + \frac{GMm}{R}$
$= \frac{GMm}{2R} = \frac{gR^2m}{2R} = \frac{mgR}{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].