Question

A liquid flows through a horizontal hose pipe of radius $0.5cm$ at a speed of $1m/s$. If the liquid is to come out of the pipe with a speed of $5m/s$ then the diameter of the nozzle should be

• A. $(\sqrt{5}+1)cm$
  
• B. $\sqrt{5}cm$
  
• C. $(\sqrt{5}-1)cm$
  
• D. $\frac{1}{\sqrt{5}}cm$
  

Answer 1

The correct option is D $\frac{1}{\sqrt{5}}cm$


From the equation of continuity,

$A_1{v}_1=A_2{v}_2$

$\frac{\pi }{4}(2\times 0.5{)}^2\times 1=\frac{\pi }{4}(D^2)\times 5$

$D^2=\frac{1}{5}$

$D=\frac{1}{\sqrt{5}}cm$

Final Answer: $\left(a\right)$