A : During orbital motion of planet around the sun work done by the centripetal force is not zero at all points on the orbit .
R : Planet is revolving around the sun in elliptical orbit .

Options

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. If both Assertion and Reason are false statement , then mark (4)

Answer

To solve the given problem, we need to analyze the assertion (A) and the reason (R) provided in the question.

### Step-by-Step Solution:

1. **Understanding the Assertion (A)**:
- The assertion states that during the orbital motion of a planet around the sun, the work done by the centripetal force is not zero at all points on the orbit.
- In circular motion, the centripetal force does not do work because the force is always perpendicular to the displacement of the object. However, in an elliptical orbit, the distance from the sun changes as the planet moves along its path.

2. **Understanding the Reason (R)**:
- The reason states that the planet is revolving around the sun in an elliptical orbit.
- In an elliptical orbit, the distance between the planet and the sun varies, which means the radius (r) changes as the planet moves. This variation in distance affects the work done by the centripetal force.

3. **Analyzing Work Done by Centripetal Force**:
- The work done (W) by a force is given by the formula:
\[ W = F \cdot d \cdot \cos(\theta) \]
where \(F\) is the force, \(d\) is the displacement, and \(\theta\) is the angle between the force and the displacement vector.
- In the case of centripetal force, it acts towards the center of the orbit (the sun), and the displacement of the planet is tangential to the orbit. Therefore, the angle \(\theta\) is 90 degrees, making \(\cos(90^\circ) = 0\). Hence, the work done by the centripetal force is zero in a circular orbit.
- However, in an elliptical orbit, the radius changes, which means the centripetal force does not remain constant, and thus the work done can be non-zero at different points of the orbit.

4. **Conclusion**:
- Since the assertion (A) is true (work done by centripetal force is not zero at all points in an elliptical orbit) and the reason (R) is also true (the orbit is elliptical), and the reason correctly explains the assertion, we conclude that both statements are true and the reason is the correct explanation of the assertion.

### Final Answer:
Both A and R are true, and R is the correct explanation of A.

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