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Assertion : In planetary motion angular ...

Assertion : In planetary motion angular momentum of planet about centre of sun remains constant. But linear momentum of system does not remain constant.
Reason : Net torque on planet any point is zero.

A

If both Assertion and Reason are true and the Reason is correct explanation of the Assertion.

B

If both Assertion and Reason are true but Reason is not the correct explantion of Assertion.

C

If Assertion is true, but the Reason is false.

D

If Assertion is false but the Reason is true.

Text Solution

AI Generated Solution

The correct Answer is:
To solve the question, we need to analyze both the assertion and the reason provided, and determine their validity. ### Step 1: Understanding the Assertion The assertion states that in planetary motion, the angular momentum of a planet about the center of the Sun remains constant, while the linear momentum of the system does not remain constant. - **Angular Momentum**: In a gravitational field, the angular momentum \( L \) of a planet about the Sun can be expressed as: \[ L = r \times p \] where \( r \) is the position vector from the Sun to the planet and \( p \) is the linear momentum of the planet. Since there is no external torque acting on the planet about the Sun, the angular momentum remains constant. - **Linear Momentum**: The linear momentum \( p \) of the planet is given by: \[ p = mv \] where \( m \) is the mass of the planet and \( v \) is its velocity. In elliptical orbits, the speed of the planet changes as it moves closer to or farther from the Sun. Therefore, the linear momentum is not constant. ### Step 2: Understanding the Reason The reason states that the net torque on the planet about any point is zero. - **Torque**: The torque \( \tau \) about a point is given by: \[ \tau = r \times F \] where \( F \) is the force acting on the planet. In the case of planetary motion, the gravitational force acts along the line joining the planet and the Sun. The angle between the position vector and the force vector is 180 degrees, leading to: \[ \tau = r \cdot F \cdot \sin(180^\circ) = 0 \] This means that the torque about the Sun is indeed zero. However, the reason claims that this is true for any point, which is not correct. The torque may not be zero when calculated about points other than the Sun. ### Step 3: Conclusion - The assertion is true: Angular momentum remains constant while linear momentum does not. - The reason is false: The net torque is not zero about any point, only about the Sun. Thus, the correct answer is that the assertion is true, but the reason is false. ### Final Answer Assertion is true, Reason is false.

To solve the question, we need to analyze both the assertion and the reason provided, and determine their validity. ### Step 1: Understanding the Assertion The assertion states that in planetary motion, the angular momentum of a planet about the center of the Sun remains constant, while the linear momentum of the system does not remain constant. - **Angular Momentum**: In a gravitational field, the angular momentum \( L \) of a planet about the Sun can be expressed as: \[ L = r \times p ...
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