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

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

Assertion $A$ : The escape velocities of planet $A$ and $B$ are same. But $A$ and $B$ are of unequal mass.

Reason $R$ : The product of their mass and radius must be same. ${M}_{1}{R}_{1} = {M}_{2}{R}_{2}$ In the light of the above statements, choose the most appropriate answer from the options given below :

Options

ABoth $A$ and $R$ are correct and $R$ is the correct explanation of $A$
BBoth $A$ and $R$ are correct but $R$ is NOT the correct explanation of $A$
C $A$ is not correct but $R$ is correct
D $A$ is correct but $R$ is not correct

Correct answer

D. $A$ is correct but $R$ is not correct

Step-by-step solution

${V}_{e} = \sqrt{\dfrac{2GM}{R}}$

$\dfrac{{M}_{1}}{{R}_{1}} = \dfrac{{M}_{2}}{{R}_{2}}$

${M}_{1}{R}_{2} = {M}_{2}{R}_{1}$

Hence reason $R$ is not correct.

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