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The distance of separation of two spheres of masses m and 5m and radius r and 2r in space is 12r if they attract each other due to gravitational forces then the distance coveres by the smaller sphere before collison is?
Since there is no external force acting on the system of two masses M and 5M. Thus the centre of mass of the system will remain unaltered.Considering mass M to be initially at the origin, The CM will beX = (0×M + 5M×12R)/(5M+M)=> X = 10RThus CM is at a distance 10R which remains unchanged before and after collision.At collision the centre of the spherical masses will be 3R apart from each otherNow let the collision take place at a distance x from the origin After collision=> {mx + 5m(x+3R)}/6m = 10R=> 6x + 15R = 60R=> 6x = 45R=> x = 7.5R
Since there is no external force acting on the system of two masses M and 5M. Thus the centre of mass of the system will remain unaltered.
Considering mass M to be initially at the origin, The CM will be
X = (0×M + 5M×12R)/(5M+M)
=> X = 10R
Thus CM is at a distance 10R which remains unchanged before and after collision.
At collision the centre of the spherical masses will be 3R apart from each other
Now let the collision take place at a distance x from the origin
After collision
=> {mx + 5m(x+3R)}/6m = 10R
=> 6x + 15R = 60R
=> 6x = 45R
=> x = 7.5R
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