A Projectile Is Launched from the Surface of a Planet $\left[ \frac { 4 G M } { 3 R } \right] ^ { 1 / 2 }$

Multiple Choice

A projectile is launched from the surface of a planet (mass = M,radius = R) .What minimum launch speed is required if the projectile is to rise to a height of 2R above the surface of the planet? Disregard any dissipative effects of the atmosphere.

A) $\left[ \frac { 4 G M } { 3 R } \right] ^ { 1 / 2 }$
B) $\left[ \frac { 8 G M } { 5 R } \right] ^ { 1 / 2 }$
C) $\left[ \frac { 3 G M } { 2 R } \right] ^ { 1 / 2 }$
D) $\left[ \frac { 5 G M } { 3 R } \right] ^ { 1 / 2 }$
E) $\left[ \frac { G M } { 3 R } \right] ^ { 1 / 2 }$