Question

A test tube filled with a liquid of density $\rho$ rotates about the vertical axis with an angular velocity $\omega$. A small ball of radius 'r' and density $\sigma$ is placed at a distance x from the axis of rotation. The radial acceleration of the ball is found to be $\frac{n\rho w^{2}x}{\sigma r}$ the value of $12$n is?

Answer 1

A test tube filled with a liquid whose density $=\rho$

Angular velocity $=\omega$

Radius$=r$ of the small ball

Density $=6$

Distance $=x$

Radial acceleration of the ball is found$=\frac{n\rho {\omega }^{2}x}{6r}$

The value of $12n$

Height of the liquid,

$H=\frac{{\omega }^2{l}^2}{2g}$

Radial acceleration

$a=\frac{d^{2}H}{d{t}^2}=\frac{\rho \times d^{2}1/r}{4\times {\omega }^2\times l^2/2}=\frac{n\rho {\omega }^{2}x}{6r}$