Question

A trolley filled with sand moves on a smooth horizontal surface with a velocity V0 . A small hole is made at the base of it from which sand is leaving out vertically down at constant rate. As the sand leaves out

As the sand leaves out

a. the velocity of the trolley remains constant

b. the velocity of the trolley increases

c. the velocity of the trolley decreases

d. the momentumof trolley + leakedout sand is conserved

• A. a & b are correct
• B. c & d are correct
• C. a & c are correct
• D. b & d are correct

Answer 1

The correct option is D

b & d are correct

Along horizontal direction, there is no action of external force on the system of trolley, its linear momentum can be conserved .

Let M $V_0$ ($\hat{i}$) = M' $V_0^{\prime }$ (i)

$\Rightarrow$ $V_0$ ' = $\frac{M{V}_0}{M^{\prime }}$

As M' is less than M, its velocity increases.

By talking trolley, leaked out sand and earth as a system, we can conserve the momentum of trolley and leaked out sand