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A: The speed of a planet is maximum at...

A: The speed of a planet is maximum at perihelion .
R : The angular momentum of a planet about centre of sun is conserved .

A

If both Assertion & Reason are true . And the reason is the correct explanation of the assertion , then mark (1)

B

If both Assertion & Reason are true but the reason is not the correct explanation of the assertion , then mark (2)

C

If Assertion is true statement but Reason is false , then mark (3)

D

It will move the same speed , tangentially to the spacecraft

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion (A) and the reason (R) provided: ### Step 1: Understand the Assertion (A) The assertion states that "The speed of a planet is maximum at perihelion." - **Explanation**: In an elliptical orbit, the perihelion is the point where the planet is closest to the Sun. According to Kepler's laws of planetary motion, a planet moves faster when it is closer to the Sun due to the stronger gravitational pull at that point. Thus, the speed of the planet is indeed maximum at perihelion. ### Step 2: Understand the Reason (R) The reason states that "The angular momentum of a planet about the center of the Sun is conserved." - **Explanation**: Angular momentum (L) is given by the formula \( L = mvr \), where \( m \) is the mass of the planet, \( v \) is its velocity, and \( r \) is the distance from the Sun. In the absence of external torques, the angular momentum of a planet in orbit remains constant. This conservation of angular momentum is a fundamental principle in physics. ### Step 3: Relate Assertion and Reason Now, we need to see if the reason supports the assertion. - Since the angular momentum is conserved, when the planet is at perihelion (where \( r \) is minimum), the velocity \( v \) must be maximum to keep the product \( mvr \) constant. This directly supports the assertion that the speed of the planet is maximum at perihelion. ### Conclusion Both the assertion (A) and the reason (R) are correct, and the reason explains the assertion. Therefore, the correct answer is that both A and R are true, and R is the correct explanation for A. ### Final Answer Both the assertion and reason are correct, and the reason explains the assertion. ---
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