A planet revolving in elliptical orbit has :
(A) a constant velocity of revolution.
(B) has the least velocity when it is nearest to the sun.
(C) its areal velocity is directly proportional to its velocity.
(D) areal velocity is inversely proportional to its velocity.
(E) To follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:
(A) a constant velocity of revolution.
(B) has the least velocity when it is nearest to the sun.
(C) its areal velocity is directly proportional to its velocity.
(D) areal velocity is inversely proportional to its velocity.
(E) To follow a trajectory such that the areal velocity is constant.
Choose the correct answer from the options given below:
- (A)C only
- (B)A only
- (C)D only
- (D)E only✓ Correct
Answer: (D)
Solution
The gravitational pull on the planet always points towards the sun, so its torque about the sun vanishes and the angular momentum of the planet stays constant. The area swept out per unit time is , which is therefore the same everywhere on the orbit; this is Kepler's second law. The speed is not constant: it is largest at the point of closest approach and smallest at the farthest point. Because the areal velocity is fixed while the speed varies, it is neither directly nor inversely proportional to the speed. The one true statement is that the planet follows a trajectory for which the areal velocity is constant.
JEE Main · 2021 · 26 Feb 2021 · Shift 1 · Single correct option