Question

A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the side. If the radius of the vessel is $5cm$ and the speed of rotation is $4$ rev/s, then the difference in the height of the liquid at the centre of the vessel and its sides is

• A. $8cm$
• B. $2cm$
• C. $40cm$
• D. $4cm$

Answer 1

The correct option is A $8cm$

Then $r=0.05m$

$\omega =4rev/sec\times 2\pi$

$\rho gh=\frac{1}{2}\rho {\left(r\omega \right)}^2$

$h=\frac{r^2{\omega }^2}{2g}=\frac{{\left(0.05\right)}^2\times {\left(4\right)}^2\times {\left(2\pi \right)}^2}{2\times 10}=8㎝$

$\Rightarrow h=8㎝$