Question

A right circular cylinder of specific gravity 0.9 is floating in the water. What is the minimum ratio of radius to height (r/h) so that it will float in water with end faces horizontal in stable equilibrium ?

• A. $\ge$ 0.234
• B. $\ge$ 0.424
• C. $\ge$ 0.628
• D. None of above

Answer 1

The correct option is B $\ge$ 0.424


$F_B=W$

$Y_w{h}_1\pi r^2=0.9y_w\pi r^{2}h$

$h_1=0.9h$

Now, MG = MB - BG

$MB=\frac{I}{V}=\frac{\pi r^4/4}{h_1\pi r^2}=\frac{r^2}{4h_1}=\frac{r^2}{3.6h}$

$BG=\frac{h}{2}-\frac{h_1}{2}=\frac{h}{2}-\frac{0.9h}{2}=\frac{0.1h}{2}$

For stable equlibrium,
$MG\ge 0$

$\Rightarrow MB-BG\ge 0$

$\frac{r^2}{3.6h}-\frac{0.1h}{2}\ge 0$

${\left(\frac{r}{h}\right)}^2\ge 0.18$

$\frac{r}{h}\ge 0.424$