Question

A very powerful vacuum cleaner which has a hose of circular cross section can lift a brick of mass 12 kg when the hose is placed perpendicularly on a horizontal flat smooth face of a brick. What is the minimum radius the hose opening should have to achieve this?
A). 1.9 cm
B). 2.6
C). 1.4 cm
D). 3.2 cm

Answer 1

Answer:

A). 1.9 cm

Explanation:

m = Mass of brick = 12 kg

g = Acceleration due to gravity = 9.81 m/s²

r = Radius of hose

A = Area = $\pi r^2$

F = Force = $mg$

Let us assume that the pressure required to lift the brick would be atmospheric pressure

$P=\dfrac{F}{A}\\\Rightarrow P=\dfrac{F}{\pi r^2}\\\Rightarrow r=\sqrt{\dfrac{F}{\pi P}}\\\Rightarrow r=\sqrt{\dfrac{12\times 9.81}{\pi\times 101325}}\\\Rightarrow r=0.01923\ m=1.9\ cm$

The radius of the hose should be 1.9 cm