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 planets $A$ and $B$ are the same, but $A$ and $B$ are of unequal masses.

Reason $R$ : The product of their mass and radius must be the same $i.e.M_A{R}_A=M_B{R}_B$.

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

The correct option is B $A$ is correct, but $R$ is not correct.

We know that, escape velocity,

$v_e=\sqrt{\frac{2GM}{R}}$

The escape velocities of planets can be equal and their masses and radii can be unequal.

So, for same $v_e$,

$\frac{M_A}{R_A}=\frac{M_B}{R_B}\Rightarrow M_A{R}_B=M_B{R}_A$

Therefore, $A$ is correct, but $R$ is not correct.