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 leaking 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 sand bag is empty?
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Answer 1

Explanation:

Answer

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

⇒=v

2

=

M

(M+m)

v

1

=

300

300+25

×27×

18

5

=8.215m/s