JEE Main 2023 · 6 April · evening · Single correct · +4 / −1
Choose the incorrect statement from the following:
- (a) The linear speed of a planet revolving around the sun remains constant.
- (b) When a body falls towards earth, the displacement of earth towards the body is negligible.
- (c) The speed of satellite in a given circular orbit remains constant.
- (d) For a planet revolving around the sun in an elliptical orbit, the total energy of the planet remains constant.
Answer and solution
Answer (a) The linear speed of a planet revolving around the sun remains constant.
Solution
Physics sir · 2 steps
Planets move in ellipses, so they speed up near the sun and slow down far away, not at a constant speed.
- Elliptical orbit. Kepler's second law says the line from the sun to a planet sweeps equal areas in equal times. Equivalently, angular momentum L = mvr is conserved at perihelion and aphelion, since there the velocity is perpendicular to the radius.
vₚ rₚ = vₐ rₐ ⇒ rₚ < rₐ gives vₚ > vₐ
Statement Physics behind it Verdict (a) Planet's linear speed constant r changes along an ellipse, so v must change to keep mvr fixed incorrect (b) Earth's displacement negligible Equal and opposite forces, but a = F/M and Mₑₐᵣₜₕ is enormous correct (c) Satellite speed in circular orbit constant r is fixed, so v = √(GM/r) is fixed correct (d) Total energy in elliptical orbit constant Gravity is a conservative force, so K + U stays fixed correct - So. The incorrect statement is (a): a planet moves fastest at perihelion and slowest at aphelion.
The idea to keep. In any orbit, total energy and angular momentum are conserved. Speed stays constant only when the distance from the centre stays constant, that is, in a circular orbit.
Answer from the NTA final answer key. Solution by PrepWiser.