Gravitation

JEE Main level, single correct, medium

172 of 223

Question 172 of 223

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 :

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Answer: (B) Both (A) and (R) are correct and (R) is the correct explanation of A.

It is known that
ω=2πT⇒ω∝1T\omega =\dfrac{2\pi }{T}\Rightarrow \omega \propto \dfrac{1}{T}
As,

Tmoon≈27{T}_{\text{moon}}\approx 27 days
Tearth≈365{T}_{\text{earth}}\approx 365 days
⇒ωmoon>ωearth\Rightarrow {\omega }_{\text{moon}}\gt {\omega }_{\text{earth}}
Hence, Both the assertion and the reason are correct and the reason is the correct explanation for the assertion.

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