The escape velocity of a body on a planet depends on

CONCEPT:

• Escape velocity: Escape velocity is the minimum velocity required by an object to escape the gravitational field.
  • For earth the escape velocity v_e = 11.2 km/s.

The escape velocity of an object is given by

\({{\rm{v}}_{\rm{e}}} = \sqrt {\frac{{2{\rm{\;G\;M}}}}{{\rm{R}}}} \), Where G is universal gravitational constant, M = mass of the planet, R = radius of the planet.

\({{\rm{v}}_{\rm{e}}} = \sqrt {{2\rm{g\;R}}} \), Where g is the gravitational acceleration of the planet.

EXPLANATION:

• From the above equation of escape velocity, we can say:

\({{\rm{v}}_{\rm{e}}} = \sqrt {\frac{{2{\rm{\;G\;M}}}}{{\rm{R}}}} \), Where G is universal gravitational constant, M = mass of the planet, R = radius of the planet.

\({{\rm{v}}_{\rm{e}}} = \sqrt {{2\rm{g\;R}}} \), Where g is the gravitational acceleration of the planet.

• Escape velocity is proportional to the radius of the planet. So option 1 follows.
• Escape velocity is proportional to the mass of the planet. So option 2 follows.
• Escape velocity is proportional to the gravity of the planet. So option 3 follows.
• All of the above statements are true, so option 4 follows.

So option 4 is correct.