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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

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The correct Answer is:
To solve the question regarding Kepler's third law of planetary motion and the associated reasoning, we will analyze both the assertion (A) and the reason (R) step by step. ### Step-by-Step Solution: 1. **Understanding the Assertion (A)**: - The assertion states that "Kepler's third law of planetary motion is valid only for inverse square forces." - Kepler's third law states that the square of the period of revolution (T²) of a planet is directly proportional to the cube of the semi-major axis (r³) of its orbit around the sun. Mathematically, this can be represented as: \[ T^2 \propto r^3 \] - This law is derived under the assumption that the gravitational force acting between the sun and the planet is an inverse square law force, which is given by Newton's law of gravitation: \[ F = \frac{G \cdot m_1 \cdot m_2}{r^2} \] - Therefore, the assertion is **true**. 2. **Understanding the Reason (R)**: - The reason states that "Only inverse square forces are always central." - A central force is defined as a force that is directed towards a fixed point (the center) and whose magnitude depends only on the distance from that point. While gravitational forces are indeed central forces, not all central forces are inverse square forces. For example, a force that varies with the distance as \( F \propto \frac{1}{r^n} \) for \( n \neq 2 \) can also be a central force. - Therefore, the reason is **false**. 3. **Conclusion**: - Since the assertion is true and the reason is false, the correct option is that the assertion is true, but the reason is false. ### Final Answer: - The assertion (A) is true, and the reason (R) is false.
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