The escape velocity for a planet is `v_e`. 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 its centre. Its speed at the centre of the planet will be

Options

A. `sqrt(1.5)V_(e)`
B. `(V_(e))/(sqrt(2))`
C. `v_(e)`
D. zero

Answer

A

Explanation

From mechanical energy conservation, `0+0=(1)/(2)mv^(2)-(3"GMm")/(2R)impliesv=sqrt((3"GM")/("R"))=sqrt(1.5)V_(e)`.