Question

A wide cylindrical vessel $50cm$ in height is filled with water and rests on a table, then find the maximum distance $l_{max}$.

• A. $l_{max}=50cm$
• B. $l_{max}=40cm$
  
• C. $l_{max}=30cm$
  
• D. $l_{max}=25cm$
  

Answer 1

Answer: (A)

$l_{max}=50cm$

$Letxbetheheightfromthebottomvelocityofefflux=\sqrt{2g(H-x)}$

$Timetakentoreachbottom=\sqrt{\frac{2x}{g}}$

$horizontaldisplacementofwater=vt=\sqrt{2g(H-x)}\times \sqrt{\frac{2x}{g}}$

$l=2\sqrt{x(H-x)}$

$tomaximizel,differentiateandequateto0.$

$\therefore \frac{dl}{dx}=\frac{2}{2\sqrt{x(H-x)}}(H-2x)=0\Rightarrow x=\frac{H}{2}=\frac{50cm}{2}=25cm$

$\therefore l_{max}=2\sqrt{25(50-25)}=50cm.$