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

This problem requires understanding angular velocity in the context of celestial orbits, specifically the Moon around the Earth and the Earth around the Sun.

Angular Velocity Defined:

• Angular velocity (\(\omega\)) is the rate at which an object rotates or revolves, measured in radians per second.
• It is calculated using the formula \(\omega = \frac{2\pi}{T}\), where \(T\) is the period of revolution.

Orbital Periods:

• The Moon's orbital period around the Earth (\(T_{\text{moon}}\)) is approximately 27.3 days.
• The Earth's orbital period around the Sun (\(T_{\text{earth}}\)) is approximately 365.25 days.

Because \(T_{\text{moon}}<T_{\text{earth}}\), the Moon's angular velocity is greater, as demonstrated by the equation: \(\omega_{\text{moon}} = \frac{2\pi}{T_{\text{moon}}} > \frac{2\pi}{T_{\text{earth}}} = \omega_{\text{earth}}\)

Assertion and Reason Analysis:

• Assertion (A): The angular velocity of the Moon orbiting the Earth exceeds that of the Earth orbiting the Sun. This statement is accurate based on the calculations.
• Reason (R): The Moon completes its orbit around the Earth in less time than the Earth takes to orbit the Sun. This statement is also accurate and correctly explains why the Moon possesses a higher angular velocity.

Therefore, the correct conclusion is: Both Assertion (A) and Reason (R) are true, and Reason (R) provides a valid explanation for Assertion (A).