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 :

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

Both (A) and (R) are correct but (R) is not the correct explanation of (A)

(A) is correct but (R) is not correct

(A) is not correct but (R) is correct

Gravitation PYQ — JEE Main 2024 · 27 Jan · Shift 2 · Q66 with Solution

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Correct answer: C

Write the relation for angular speed

Angular speed is

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

where $T$ is the time period of revolution.

For the moon around the earth

The moon completes one revolution around the earth in about

T_m \approx 27.3\ \text{days}

So its angular speed is

\omega_m = \frac{2\pi}{27.3\ \text{days}}

For the earth around the sun

The earth completes one revolution around the sun in about

T_e \approx 365\ \text{days}

So its angular speed is

\omega_e = \frac{2\pi}{365\ \text{days}}

Compare the two angular speeds

Since

27.3 < 365

therefore

\frac{2\pi}{27.3} > \frac{2\pi}{365}

Hence,

\omega_m > \omega_e

So Assertion (A) is correct.

Check the Reason (R)

Reason says: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.

This is true because

27.3\ \text{days} < 365\ \text{days}

So Reason (R) is also correct.

Does Reason explain Assertion?

Yes. Since angular speed is inversely proportional to time period:

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

A smaller time period means greater angular speed. Therefore, because the moon takes less time to revolve, its angular speed is greater.

So (R) is the correct explanation of (A).

Therefore, the correct option is:

\boxed{\text{C}}

More from Gravitation

View written solutionFree

Correct answer: C

Write the relation for angular speed

Angular speed is

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

where $T$ is the time period of revolution.

For the moon around the earth

The moon completes one revolution around the earth in about

T_m \approx 27.3\ \text{days}

So its angular speed is

\omega_m = \frac{2\pi}{27.3\ \text{days}}

For the earth around the sun

The earth completes one revolution around the sun in about

T_e \approx 365\ \text{days}

So its angular speed is

\omega_e = \frac{2\pi}{365\ \text{days}}

Compare the two angular speeds

Since

27.3 < 365

therefore

\frac{2\pi}{27.3} > \frac{2\pi}{365}

Hence,

\omega_m > \omega_e

So Assertion (A) is correct.

Check the Reason (R)

Reason says: The moon takes less time to move around the earth than the time taken by the earth to move around the sun.

This is true because

27.3\ \text{days} < 365\ \text{days}

So Reason (R) is also correct.

Does Reason explain Assertion?

Yes. Since angular speed is inversely proportional to time period:

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

A smaller time period means greater angular speed. Therefore, because the moon takes less time to revolve, its angular speed is greater.

So (R) is the correct explanation of (A).

Therefore, the correct option is:

\boxed{\text{C}}

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