Analyse the given statements and choose the correct option.

Statement 1: The escape velocities of planet A and B are same. But A and B are of unequal mass.

Statement 2: The product of their mass and radius must be same. M₁R₁ = M₂R₂

In the light of the above statements, choose the most appropriate answer from the options given below :

CONCEPT:

Escape velocity is defined as the speed at which an object travels to break the gravity of the moon or planet without the development of propulsion and it is written as;

\(v_c = \sqrt {\frac{2GM}{r}}\)

Here we have G as the gravitational constant, M as the mass of the body, r is the distance and v_c is the escape velocity.

EXPLANATION:

Assertion A said that the escape velocities of the planets A and B are the same but their masses are unequal so there is a change they are having different distances which makes their escape velocity equal. Therefore, Assertion A is correct.

Reason R says that the product of their mass and radius must be the same M₁R₁ = M₂R₂

According to the formulation of the escape velocity we have;

\(v_c = \sqrt {\frac{2GM}{r}}\)

For two bodies it is written as;

\(\frac{M_1}{R_1}= \frac{M_2}{R_2}\)

⇒ M1R2 = M2R1

Therefore, reason R is incorrect.

Hence, option 3) is the correct answer.