A hole is drilled from the surface of earth to its center. A particle is dropped from rest at the surface of earth . The speed of the particle when it reaches the center of the earth in terms of escape velocity of the surface of earth $v_e$ is

Question

$$(a)\;\frac{v_e}{2} \quad (b)\;v_e \quad (c)\; \sqrt 2 v_e \quad (d)\;\frac{v_e}{\sqrt 2}$$