An experiment is performed in deep space with two uniform spheres, one with mass 24 kilogram and the other with mass 100 kilogram. They have equal radii, r= 0.40 meter. The spheres are released from rest with their centers a distance 37 meter apart. They accelerate toward each other because of their mutual gravitational attraction. You can neglect all gravitational forces other than that between the two spheres.
1. When their centers are a distance 25 meter apart, obtain the speed of the 24 kilogram sphere.
2. Obtain the speed of the sphere with mass 100 kilogram.
3. Obtain the magnitude of the relative velocity with which one sphere is approaching to the other.
4. Find how far from the initial position of the center of the 24 kg sphere do the surfaces of the two spheres collide?