Choose the incorrect statement from the given statements.
- Planets revolve around the Sun with constant linear speed.
- Energy of the planet in elliptical orbit is constant.
- Satellites in circular motion have constant energy.
- Body falling towards the Earth results in negligible displacement of the Earth.
The Correct Option is A
Approach Solution - 1
The correct answer should be Planet revolves around the Sun in elliptical orbit with variable speed.
Approach Solution -2
The incorrect statement from the given options is: Planets revolve around the Sun with constant linear speed.
This statement is incorrect because planets actually revolve around the Sun with constant angular speed, not linear speed. This is because the distance between the planet and the Sun changes as the planet moves along its elliptical orbit. According to Kepler's second law, the line joining the planet and the Sun sweeps out equal areas in equal time intervals, which implies that the planet moves faster when it is closer to the Sun and slower when it is farther away from the Sun. Therefore, the angular speed of the planet remains constant, while the linear speed varies throughout its orbit.
Hence, the correct option is (A) Planets revolve around the Sun with constant linear speed.
Answer. A
Approach Solution -3
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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].