Assertion : Angular velocity of moon revolving about earth is more than angular velocity of earth revolving around sun.

Reason : Time taken by moon to revolve around earth is less than time taken by earth to revolve around sun.

Correct Option: Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)

Let us analyze the Assertion and the Reason step-by-step:

1. Analysis of the Assertion:
The angular velocity ($\omega$) of a body in a circular or near-circular orbit is given by the relation:
$\omega =\frac{2\pi }{T}$
where $T$ is the time period of revolution.

Let the time period of the Moon revolving around the Earth be $T_{\text{moon}}$. The Moon takes approximately 27.3 days to complete one revolution around the Earth.
Let the time period of the Earth revolving around the Sun be $T_{\text{earth}}$. The Earth takes approximately 365.25 days to complete one revolution around the Sun.

Since $T_{\text{moon}}<T_{\text{earth}}$, we can compare their angular velocities:
${\omega }_{\text{moon}}=\frac{2\pi }{T_{\text{moon}}}$
and
${\omega }_{\text{earth}}=\frac{2\pi }{T_{\text{earth}}}$

Since the time period of the Moon is much smaller than the time period of the Earth, its angular velocity is much larger:
${\omega }_{\text{moon}}>{\omega }_{\text{earth}}$
Therefore, the Assertion is true.

2. Analysis of the Reason:
The Reason states that the time taken by the Moon to revolve around the Earth (about 27.3 days) is less than the time taken by the Earth to revolve around the Sun (about 365.25 days). This statement is factually true.

3. Verification of Explanation:
Because the angular velocity is inversely proportional to the time period of revolution ($\omega \propto \frac{1}{T}$), the smaller time period of the Moon's revolution directly explains why the Moon has a higher angular velocity than the Earth.
Thus, the Reason is the correct explanation of the Assertion.