A planet of radius R has an acceleration due to gravity of gₑ on its surface A deep smooth tunnel is dug in this planet radially inward to reach a point p.p located at a distance of R₂ from the center of the planet. Assume that the planet has uniform density. The kinetic energy required to be given to a small body of mass m projected radially outward from p, so that it gains a maximum altitude equal to thrice the radius of the planet from its surface id equal to

A 6316mg₂R
B 38mg₂R
C 98mg₂R
D 2116mg₂R