Question

The escape velocity of a body depends upon mass as

• A. $m^0$
• B. $m^2$
• C. $m^1$
• D. $m^3$

Answer 1

The correct option is A

$m^0$

1. The escape velocity of an object like a satellite, is the minimum speed that the object must acquire to escape or move an infinite distance from the gravitational force of a body like earth, from where the object is projected.
2. Using formula;$V_{esc}=\sqrt{2gR}$,
3. Where G is the gravitational constant and R is the radius of the planet.
4. Escape velocity,
   ${\displaystyle v_e=\sqrt{2gR}=\sqrt{\frac{2GM}{R}}}$
   ${\displaystyle \Rightarrow v_e\propto m^0}$
   In this, expression the mass of the body (m) is not present, hence escape velocity is independent of the mass.

Hence, the correct option is (a).