Import Question JSON

$\text{Hint: The planet revolves around the Sun in an elliptical orbit with variable speed.}$ $\text{Step: Identify the incorrect statement.}$ $\text{(A) Planets revolve around the Sun with constant linear speed.}$ $\text{While planets have constant angular velocity in their elliptical orbits, their linear speed actually varies as they move closer or further away from the Sun. As per Kepler's second law, the area swept by the radius vector from the Sun to a planet in a fixed time interval is constant. This means the planet's speed is higher when it's closer to the Sun (perihelion) and slower when it's farther away (aphelion). The statement is incorrect.}$ $\text{(B) The energy of a planet in an elliptical orbit is constant.}$ $\text{This is true because the total mechanical energy (sum of kinetic and potential energy) of a planet in an elliptical orbit remains constant throughout its orbit. This statement is correct.}$ $\text{(C) A satellite in circular motion has constant energy.}$ $\text{Similarly, a satellite in a circular orbit maintains a constant total mechanical energy due to the balance between its kinetic and potential energy. This statement is correct.}$ $\text{(D) A body falling towards the Earth results in negligible displacement of the Earth.}$ $\text{This statement reflects the concept of inertia. While Earth and the falling body attract each other with equal and opposite forces, the Earth's massive size compared to the object makes its displacement practically negligible. This statement is correct.}$ $\text{Therefore, only statement (A) is incorrect because planets exhibit varying linear speeds despite having constant angular velocity in their elliptical orbits.}$ $\text{Hence, option (1) is the correct answer.}$