JEE Physics 2023 Question with Solution

Given: Four statements about planetary motion in an elliptical orbit around the sun.

Find: Which statements are correct.

Use Newton's law of gravitation and Kepler's third law.

So, the gravitational force is inversely proportional to the square of the distance:

Hence, statement A is correct.

Also, from the same relation, force is directly proportional to the product of the masses:

Therefore, statement B is incorrect because it says inversely proportional.

This gravitational force provides the centripetal force and acts towards the sun, not away from it. Therefore, statement C is incorrect.

By Kepler's third law:

So, statement D is correct.

Therefore, the correct option is A.

1. Statement A: Newton's law of universal gravitation shows that gravitational force varies as $\frac{1}{r^2}$, so this statement is true.

2. Statement B: The gravitational force depends directly on the product $m_1 m_2$, so calling it inversely proportional is false.

3. Statement C: Centripetal force is always directed towards the center of revolution, here the sun, so this statement is false.

4. Statement D: Kepler's third law states:

Thus this statement is true.

So the true statements are A and D only, which corresponds to option A.