JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Gravitation

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 :

Answer: (A)

Solution

Escape velocity is given by

v_{e} = \frac{2 GM}{R}

. For two planets to have equal escape velocities:

(v_{e})_{A} = (v_{e})_{B} \Rightarrow \frac{M _{1}}{R _{1}} = \frac{M _{2}}{R _{2}}

This means the ratio

M / R

must be equal, not the product

M R

. Assertion A is correct (planets can have equal escape velocities with unequal masses), but Reason R is incorrect (it should be

M_{1} / R_{1} = M_{2} / R_{2}

, not

M_{1} R_{1} = M_{2} R_{2}

JEE Main · 2021 · 25 Feb 2021 · Shift 1 · Single correct option