Given below are two statements: one is labelled as Assertion (A)...

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 :

Options

ABoth $(\mathrm{A})$ and $(\mathrm{R})$ are correct and $(\mathrm{R})$ is the correct explanation of $\mathrm{( A)}$
BBoth $(\mathrm{A})$ and $(\mathrm{R})$ are correct but $(\mathrm{R})$ is not the correct explanation of (A)
C(A) is correct but $(\mathrm{R})$ is not correct
D(A) is not correct but (R) is correct

Correct answer

A. Both $(\mathrm{A})$ and $(\mathrm{R})$ are correct and $(\mathrm{R})$ is the correct explanation of $\mathrm{( A)}$

Step-by-step solution

\frac{\mathrm{dA}}{\mathrm{dt}}=\frac{\mathrm{L}}{2 \mathrm{~m}}

Due to central force torque is zero

\&

angular momentum is constant.

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