For the cases shown in ?Fig. Q6.8?, the object is released from rest at the top and feels no friction or air resistance. In which (if any) cases will the mass have (i) the greatest speed at the bottom and (ii) the most work done on it by the time it reaches the bottom?

Solution 8DQ Step 1: (a).Consider the energy conservation principle to calculate greatest speed of the ball at bottom U +iK = i + K f f Here U and K are the potential and kinetic energy of the ball at initial and final stage. Where U = mihand K = 0 i 2 U f 0 and K = 1/2fmv mgh =½ mv 2 v = 2gh Here m is mass of ball,g is gravity and h is height. Hence,the bottom speed of ball in all cases same that is 2gh .