Question

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 sand starts checking out of a hole on the floor of the trolley at the rate of 0.05 kg s⁻¹. What is the speed of the trolley after the entire sandbag is empty?

Answer 1

read this line " A trolley of mas 300kg carrying a sandbag of 25kgis moving uniformly with a speed of 27km/h on a frictionless track."

e.g., trolley is moving uniformly with a speed of 27 km/h on a frictionless track.
means, speed of trolley is uniform. hence there does not external force act on the trolley . Even if the sand starts leaking, there is no external force on the trolley.

Hence, the speed of the trolley will not change.

so, speed of trolley after the entire sandbag is empty = 27 km/h

Answer 2

Answer:8.215m/s

Explanation:

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

v  

1

​  

= initial velocity

v  

2

​  

= final velocity ( to be found)

Then P  

1

​  

=(M+m)v  

1

​  

 when the sand bag is empty the momentum is

P  

2

​  

=(M+0)v  

2

​  

 

Momentum is conserved in horizontal direction so

P  1  =P  2 ⇒

=v2=  M (M+m)

​  

v  

1

​  

=  

300

300+25

​  

×27×  18

5

​  

=8.215m/s