Sphere of mass M and radius R is kept on a rough horizontal floor. A small particle of mass m, moving horizontally with velocity, collides with the sphere and sticks to it. Line of motion of particle before collision is at a heighth above the floor. Assume that mase of sphere is very large in comparison to particle so that we may assume that centre of mass of the combined system remains at the centre of the sphere after the collision. At what height h above the floor, particle should hit the sphere so that it may start pure rolling after the collision.

Sphere of mass M and radius R is kept on a rough horizontal floor. A s

1.	Sphere of mass M and radius R is kept on a rough horizontal floor. A small particle of mass m, moving horizontally with velocity, collides with the sphere and sticks to it. Line of motion of particle before collision is at a heighth above the floor. Assume that mase of sphere is very large in comparison to particle so that we may assume that centre of mass of the combined system remains at the centre of the sphere after the collision. At what height h above the floor, particle should hit the sphere so that it may start pure rolling after the collision.
Answer» `(5R)/(7)` `(3R)/(5)` `(3R)/(7)` `(7R)/(5)` Solution : For pure rolling we can WRITE `u=R omega` `rArr (m u)/(M)=R (5 m u(h-R))/(MR^(2))` `rArr 1=(5(h-R))/(2R)` `rArr 2R= 5(h-R)` `rArr h=(7R)/(5)` Hence option (d) is CORRECT.