50) 2 spherical bodies of mass M and 5M are of radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller bady just before collision is

a) 1.5R b)2.5R c)4.5R d)7.5R

Correct ans. d) 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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