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A : Kepler's third law of planetary mot...

A : Kepler's third law of planetary motion is valid only for inverse square forces .
R : Only inverse square forces are always central .

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 analyze the statements given in the question, we need to evaluate both the assertion (A) and the reason (R) separately. ### Step 1: Understanding Kepler's Third Law Kepler's Third Law states that the square of the period (T) of any planet is directly proportional to the cube of the semi-major axis (r) of its orbit. Mathematically, this can be expressed as: \[ T^2 \propto r^3 \] ### Step 2: Validity of Kepler's Third Law Kepler's Third Law is valid for celestial bodies that are influenced by a central force that follows the inverse square law, such as gravitational force. This means that for planets orbiting a star (like the Earth around the Sun), the law holds true because the gravitational force between the two bodies is an inverse square force. ### Step 3: Evaluating Assertion (A) The assertion states that "Kepler's third law of planetary motion is valid only for inverse square forces." This statement is correct because the derivation of Kepler's Third Law relies on the properties of inverse square forces, which are central forces. ### Step 4: Evaluating Reason (R) The reason states that "Only inverse square forces are always central." This statement is misleading. While it is true that inverse square forces are central forces, not all central forces must follow the inverse square law. There are other types of central forces that do not adhere to the inverse square law. ### Step 5: Conclusion Since the assertion (A) is correct and the reason (R) is incorrect, we conclude that the correct answer is that the assertion is true, but the reason is false. ### Final Answer - Assertion (A) is true. - Reason (R) is false.
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