Question

The escape velocity of a particle of mass $m$ varies as

• A. $m^2$
• B. $m$
• C. $m^0$
• D. $m^{-1}$

Answer 1

The correct option is C

$m^0$

The explanation for the correct option:

1. Escape velocity is defined as the minimum velocity with which a particle is projected from the surface of the planet in order to escape the gravitational attraction of that planet.
2. It is understood that the escape velocity is computed using the formula $v_e=\sqrt{\frac{2GM}{R}}$where $G,M,R$ are gravitational constant, the mass of the earth (planet), and the radius of the earth (planet) respectively.
3. From the formula, it is clear that the escape velocity doesn't depend on the mass of the particle which is projected.
4. So, it can say that the escape velocity is independent of the mass of the particle which is projected.
5. For instance, we are aware that things with various masses are not affected by the gravitational field in different ways.
6. As a body of $1kg$ will fall at the same rate as a $5kg$ body respectively, if dropped from the same height.
7. Therefore, the escape velocity of a particle of mass $m$ varies as $m^0$.

Hence, option C is the correct answer.