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) - (3GMm)/(2R) implies v= sqrt((3GM)/R)=sqrt(1.5) v_(e)`.