50) 2 spherical bodies of mass M and 5M are of radii R and 2R respectively are released in free - Physics - System Of Particles And Rotational Motion

Question

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

Somnath physics · Accepted Answer

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 = (0Ã—M + 5MÃ—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