Planet 1 hits mass 3M and radius R, while Planet 2 has mass 4M and radius 2R. Th
ID: 1562646 • Letter: P
Question
Planet 1 hits mass 3M and radius R, while Planet 2 has mass 4M and radius 2R. They are separated by center-to-center distance 8R. A rock is placed halfway between their centers at point O. It is released from rest. Ignore any motion of the planets. Derive an expression, in terms of relevant system parameters, for the magnitude of the acceleration a of the rock at the moment it is released. Towards which planet is the direction of the acceleration in part a)? The rock is released from rest at point O. Derive an expression for the speed v with which the rock crashes into a planet.Explanation / Answer
Conserving energy
KE at the point of crashing = PE at the point of release of the rock
0.5Mv^2 = Mgh = Mg×4R
Rock is at a distance 4 R from center of each planet
Hence
v = (8gR)^0.5