A uniform sphere of mass m and radius R is placed on a rough horizontal surface. The sphere is struck horizontally at a heighth from the floor. Match the following:

A uniform sphere of mass m and radius R is placed on a rough horizonta

1.	A uniform sphere of mass m and radius R is placed on a rough horizontal surface. The sphere is struck horizontally at a heighth from the floor. Match the following:
Answer» Solution : The SPHERE will roll without slipping if `omega=(v)/(R)` Moment of inertia about DIAMETER is `I=(2)/(5)MR^(2)` ANGULAR momentum of the sphere about C.M. is given by `Mv(h-R)=I omega` `=(2)/(5) MR^(2)*(v)/(R)` or `mv(h-R)=(2)/(4) MvR` or `h=(7)/(7)R` So, if force is applied at `h = (7)/(5)R` sphere will roll without slipping Torque DUE to sphere about `CM tau=F(h-R)`. sphere will have only translational motion if `t= 0 or h = R`. Sphere will spin clockwise if torque is positive and will spin anticlockwise if torque is negative. So `(a) to (III), (b) to (iv), (c) to (ii), (d) to (i)`.