Question

The escape velocity for a planet is ve. A particle starts from rest at a large distance from the planet, reaches the planet only under gravitational attraction, and passes through a smooth tunnel through it's centre. It's speed at the centre of the planet will be?

Answer 1

( 1/2 mO v^2 ) = ( G mE mO / rE ) Knowing this we can solve for velocity: v^2 = 2G mE / rE this is the escape velocity formula.

Answer 2

Ans ((1.5)^1/2)ve

Explanation:

From mechanical energy conservation

0+0= 1/2mv^2-3GMm/2R

So v=(3GM/R)^1/2 = ((1.5)^1/2)ve