Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is co

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Q.
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : The radius vector from the Sun to a planet sweeps out equal areas in equal intervals of time and thus areal velocity of planet is constant.

Reason (R) : For a central force field the angular momentum is a constant.

In the light of the above statements, choose the most appropriate answer from the options given below: [2025]

1 Both (A) and (R) are correct and (R) is the correct explanation of (A)

2 Both (A) and (R) are correct but (R) is not the correct explanation of (A)

3 (A) is correct but (R) is not correct

4 (A) is not correct but (R) is correct

Ans.
(1)

From Kepler's $2^{nd}$ law

$\frac{d A}{d t} = \frac{L}{2 m} = constant$

Due to central force torque is zero and angular momentum is constant.

Solution

1 Both (A) and (R) are correct and (R) is the correct explanation of (A)

2 Both (A) and (R) are correct but (R) is not the correct explanation of (A)

3 (A) is correct but (R) is not correct

4 (A) is not correct but (R) is correct

Ans.
(1)

From Kepler's $2^{nd}$ law

$\frac{d A}{d t} = \frac{L}{2 m} = constant$

Due to central force torque is zero and angular momentum is constant.

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Solution

1 Both (A) and (R) are correct and (R) is the correct explanation of (A)

2 Both (A) and (R) are correct but (R) is not the correct explanation of (A)

3 (A) is correct but (R) is not correct

4 (A) is not correct but (R) is correct

Ans. (1) From Kepler's 2nd law dAdt=L2m=constant Due to central force torque is zero and angular momentum is constant.

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Ans.
(1)

From Kepler's $2^{nd}$ law

$\frac{d A}{d t} = \frac{L}{2 m} = constant$

Due to central force torque is zero and angular momentum is constant.