Question

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 :

• A. Both $A$ and $R$ are correct but $R$ is $NOT $ the correct explanation of $A$
• B. $A$ is correct but $R$ is not correct
• C. Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$
• D. $A$ is not correct but $R$ is correct

Answer 1

Answer: (B)

$V _{ e }=\sqrt{\frac{2 GM }{ R }}$
$\frac{ M _{1}}{ R _{1}}=\frac{ M _{2}}{ R _{2}}$
$M _{1} R _{2}= M _{2} R _{1}$
Hence reason $R$ is not correct.