Question

Consider a rotating spherical planet. The velocity of a point on its equator is $v$. The effect of rotation of the planet is to make $g$ at the equator $1/2$ of $g$ at the pole. What is the escape velocity for a polar particle on the planet expressed as a multiple of $v$?

• A. 0.5v
• B. v
• C. $\sqrt{2}v$
• D. 2v

Hint:

Escape velocity depends on the gravitational acceleration at the surface of the planet.

Answer 1

The Correct Option is D

The escape velocity $v_e$ is given by: \[ v_e = \sqrt{2 g R} \] where $g$ is the gravitational acceleration and $R$ is the radius. The velocity at the equator is $v$, so the escape velocity is $2v$.