Question

If the piston is pushed at a speed of $5mm{s}^{-1}$, the air comes out of the nozzle with a speed of

• A. $0.1m{s}^{-1}$
• B. $1m{s}^{-1}$
• C. $2m{s}^{-1}$
• D. $8m{s}^{-1}$

Answer 1

The correct option is C $2m{s}^{-1}$

From equation of continuity: $A_1{V}_1=A_2{V}_2$
Subscript 1 stands for piston and 2 for nozzle respectively.
We have: $d_1=20mm$ and $d_2=1mm$
Therefore, $A_1=\pi \left({20}^2\right)$ and $A_1=\pi \left(1^2\right)$
Also, $V_1=5m/s$
Thus, $\pi \left({20}^2\right)\times 5=\pi \left(1^2\right)\times V_2$
$V_2=2m/s$