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

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

  1. (1) Both $A$ and $R$ are correct but $R$ is NOT the correct explanation of $A$

  2. (2) $\mathrm{A}$ is correct but $\mathrm{R}$ is not correct

  3. (3) Both $A$ and $R$ are correct and $R$ is the correct explanation of $A$

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

Correct Option: , 2

Solution:

(2)

$\mathrm{V}_{\mathrm{e}}=$ escape velocity

$v_{e}=\sqrt{\frac{2 G M}{R}}$

so for same $v_{e r} \frac{M_{1}}{R_{1}}=\frac{M_{2}}{R_{2}}$

$A$ is true but $R$ is false

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