A uniform sphere of mass (m ) and radius (R ) is placed on a rough horizontal surface (figure). The sphere is struck horizontally at a height (h ) from the floor. Match the following ( array |c|l|c|l| & Column I & & Column II (a) & h = R/2 & (p) & Sphere rolls without slipping, & & & with constant velocity and no loss of energy (b) & h = R & (q) & Sphere spins clockwise, loses energy & & & by friction (c) & h = 3R/2

Step-by-step solution

The sphere will roll without slipping when ( = v r ), where (v ) is linear velocity and ( ) is angular velocity of the sphere. Now, angular momentum of sphere, about centre of mass [We are applying conservation of angular momentum just before and after struck] ( aligned m v(h-R) & =I = ( 2 5 m R^2 ) ( v R ) m v(h-R) & = 2 5 m v R h-R & = 2 5 R h= 7 5 R aligned ) Therefore, the sphere will roll without slipping with a constant velocity and hence, no loss of energy, so ( D p ) Torque due to applied force, (F ) about