If the mass of moon is $ \frac{1}{90} $ of earths mass, its radius is $ \frac{1}{3} $ of earths radius and if $ g $ is acceleration due to gravity on earth, then the acceleration due to gravity on moon is ...... :
- $ \frac{g}{3} $
- $ \frac{g}{90} $
- $ \frac{g}{10} $
- $ \frac{g}{9} $
The Correct Option is C
Solution and Explanation
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(A) A simple pendulum is taken to a planet of mass and radius, 4 times and 2 times, respectively, than the Earth. The time period of the pendulum remains same on earth and the planet.
(R) The mass of the pendulum remains unchanged at Earth and the other planet.
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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].