Choose the incorrect statement from the following :
The linear speed of a planet revolving around the sun remains constant.
The speed of satellite in a given circular orbit remains constant.
When a body falls towards earth, the displacement of earth towards the body is negligible.
For a planet revolving around the sun in an elliptical orbit, the total energy of the planet remains constant.
Correct answer:A
Standard Method
Given: Four statements about orbital motion and gravitation.
Find: The incorrect statement.
Statement A says the linear speed of a planet revolving around the sun remains constant. By Kepler's second law, a planet sweeps equal areas in equal times in an elliptical orbit. This means the planet moves faster when closer to the Sun and slower when farther away — so its linear speed is not constant. Statement A is incorrect.
Statement B says the speed of a satellite in a given circular orbit remains constant. For a circular orbit, the net centripetal force is constant and the radius is fixed, so the speed is constant. Statement B is correct.
Statement C says the displacement of the Earth toward a falling body is negligible. Because the Earth's mass is enormously greater than the falling body's mass, the Earth's acceleration toward the body is negligible. Statement C is correct.
Statement D says the total mechanical energy of a planet in an elliptical orbit is constant. Gravity is a conservative force, so total mechanical energy is conserved. Statement D is correct.
Therefore, the incorrect statement is A, and the correct option is A.
Selecting option B because satellites in circular orbits look like candidates for variable speed. In a circular orbit the speed is constant; it is elliptical orbits where speed varies. A planet around the Sun follows an elliptical orbit, so its speed is not constant.
Confusing Kepler's second law (equal areas in equal times) with constant speed. Equal-area sweeping implies variable speed — the planet moves faster near the perihelion and slower near the aphelion.
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