Question

Assertion: The angular velocity of the moon revolving around the earth is more than that of the earth revolving around the Sun.
Reason: The time taken by the moon to revolve around the earth is less than the time taken by the earth to revolve around the sun.

• A. Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are the true but Reason (R) is not a correct explanation of Assertion (A).
• C. Assertion (A) is true and Reason (R) is false.
• D. Assertion (A) is false and Reason (R)

Answer 1

The Correct Option is A

The angular speed \( \omega \) of an object is given by:

\(\omega = \frac{2\pi}{T},\)

where \( T \) is the time period.

For the moon:
- \( T_{\text{moon}} = 27 \, \text{days} \).

For the earth:
- \( T_{\text{earth}} = 365 \, \text{days} \).

Since the moon takes less time to complete one orbit around the earth compared to the earth's revolution around the sun, \( T_{\text{moon}} < T_{\text{earth}} \). Therefore:

\(\omega_{\text{moon}} > \omega_{\text{earth}}.\)

This makes both the assertion and the reason correct, and the reason is the correct explanation of the assertion.

The correct option is (A) : Both Assertion (A) and Reason (R) are the true and Reason (R) is a correct explanation of Assertion (A).