JEE Main 2024 — Gravitation Question with Solution

The angular speed $$\omega$$ of an object in circular motion is given by the equation

$\omega =\frac{2\pi }{T}$

where $$T$$ is the period of the motion - the time it takes to make one complete revolution.

Assertion (A) states that the angular speed of the Moon in its orbit around the Earth is more than the angular speed of the Earth in its orbit around the Sun. We can compare these angular speeds by comparing their periods.

The Moon takes approximately 27.3 days to orbit the Earth (this is its sidereal period, not its synodic period, which accounts for the Earth's motion around the Sun as well). The Earth takes approximately 365.25 days to orbit the Sun. Since the period of the Moon’s orbit is much less than the period of the Earth’s orbit, the angular speed of the Moon is much larger than that of the Earth. This makes Assertion (A) correct.

Reason (R) states that the Moon takes less time to move around the Earth than the time taken by the Earth to move around the Sun. This is also correct, as the previously mentioned periods demonstrate: 27.3 days for the Moon to orbit Earth vs. 365.25 days for Earth to orbit the Sun.

Furthermore, the reason (R) directly explains why assertion (A) is true. Since angular speed is inversely proportional to the period of orbit, the fact that the Moon takes less time to complete an orbit implies it has a higher angular speed relative to the Earth’s angular speed in its orbit around the Sun.

Therefore, the correct answer is:

Option C Both (A) and (R) are correct and (R) is the correct explanation of (A)