Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A) : The angular speed of the moon in its orbit about the earth is more than the angular speed of the earth in its orbit about the sun.
Reason (R) : The moon takes less time to move around the earth than the time taken by the earth to move around the sun.
In the light of the above statements, choose the most appropriate answer from the options given below :

Solution

Physics sir · 4 steps

Angular speed is just one full turn divided by the time it takes, so the shorter period wins.

1. Link speed to period. Any body in orbit sweeps one full turn, 2π radians, in one period T. So its average angular speed depends only on that period.

   ω = 2π/T

2. Compare the periods. The moon goes round the earth in about 27.3 days, and the earth goes round the sun in about 365 days. So (R) is correct.
3. Compare the speeds. ωₘₒₒₙ = 2π/27.3 ≈ 0.23 rad day⁻¹ and ωₑₐᵣₜₕ = 2π/365 ≈ 0.017 rad day⁻¹. The moon's angular speed is about 13 times larger, so (A) is correct.
4. So. (A) follows directly from (R) through ω = 2π/T: the smaller period is exactly why the angular speed is larger. The answer is (c).

The idea to keep. For angular speed, look only at the period: ω = 2π/T. The orbit radius and the size of the bodies do not enter. Shorter period always means larger angular speed.

Answer from the NTA final answer key. Solution by PrepWiser.