Question

A cylinder of radius $R=1\text{m}$ and height $H=3\text{m}$ two-thirds filled with water, is rotated about its vertical axis as shown in Figure. Determine the speed of rotation when the water just starts spilling over the rim.

• A. $\sqrt{20}\text{rad/s}$
• B. $\sqrt{40}\text{rad/s}$
• C. $8\text{rad/s}$
• D. $40\text{rad/s}$

Answer 1

The correct option is B $\sqrt{40}\text{rad/s}$

Given that,
Height of the cylinder, $H=3\text{m}$
Initial height of the water, $h=\frac{2}{3}H=2\text{m}$
Radius of the rim, $R=1\text{m}$
$g=10{\text{m/s}}^2$

The speed of rotation of water when it starts spilling over the rim is given by
$\omega =\sqrt{\frac{4g(H-h)}{R^2}}$
$\Rightarrow \omega =\sqrt{\frac{4\left(10\right)(3-2)}{1^2}}$
$\Rightarrow \omega =\sqrt{40}\text{rad/s}$

Hence, option (b) is correct.