A trolley of mass 300 kg carrying a sandbag of 25kg is moving uniformly with a speed of 27 km/hr on a frictionless track.After a while,sand starts leaking out of a hole on the floor of the trolley at the rate of 0.05 kg per second.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 trolly.Therefore there is no force in horizontal direction hence in horizontal direction momentum is conserved.

Let M -> mass of trolley (given)

     m ->mass of sandbag (given)

     v_{1 -> initial velocity} (given)

and v₂ -> final velocity ( to be found)

then

   

put the values and get the answer