An experiment is performed in deep space with two uniform spheres, one with mass 50.0 kg and the other with mass 100.0 kg. They have equal radii, r = 0.20 m. The spheres are released from rest with their centers 40.0 m apart. They accelerate toward each other because of their mutual gravitational attraction. You can ignore all gravitational forces other than that between the two spheres.

(a) Explain why linear momentum is conserved.

(b) When their centers are 20.0 m apart, find

(i) The speed of each sphere

(ii) The magnitude of the relative velocity with which one sphere is approaching the other.

(c) How far from the initial position of the center of the 50.0-kg sphere do the surfaces of the two spheres collide?