A trolley of mass 300 kg carrying a sandbag of 25 kg is moving uniformly with a speed of 27 km/h on a frictionless track. After a while, the sand starts leaking out of a hole on the floor of the trolley at the rate of0.05 kg s–1. What is the speed of the trolley after the entire sandbag is empty?
Since the hole is on the floor , that means sand is falling vertically with respect to trolley. Therefore there is no force in horizontal direction hence in horizontal direction momentum is conserved. Let M= mass of trolley m= mass of sandbag v1= initial velocity v2= final velocity ( to be found) Then P1=(M+m)v1 when the sand bag is empty the momentum is P2=(M+0)v2 Momentum is conserved in horizontal direction so P1=P2 ⇒=v2=M(M+m)v1=300300+25×27×185=8.215m/s
