Question

A solid cylinder of length L, diameter D and specific gravity 0.6 floats in neutral equilibrium in water with its axis vertical. What is the ratio of L to D?

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{2\sqrt{3}}{5}$
• C. $\frac{4}{5\sqrt{3}}$
• D. $\frac{5}{4\sqrt{3}}$

Answer 1

The correct option is D $\frac{5}{4\sqrt{3}}$

$GM=0$

$\frac{I}{V_{Dis}}-BG=0$

$\frac{\frac{\pi D^4}{64}}{\frac{\pi D^2}{4}\times h}=\frac{L}{2}-\frac{h}{2}$

$\frac{D^2}{8h}=L-h...\left(i\right)$
Force balancing
$\text{Weight of body}=F_B$

$\left(600\right)\frac{\pi D^2}{4}\times L\times g={10}^3\times \frac{\pi D^2}{4}\times h\times g$

$h=0.6L...\left(ii\right)$
From (i) and (ii)
$\frac{D^2}{8\left(0.6L\right)}=L-0.6L$

$\frac{D}{L}=\frac{4\sqrt{3}}{5}$

$\frac{L}{D}=\frac{5}{4\sqrt{3}}$