Question

 A solid cylinder is to be 0.25 m in diameter. The base of axial length 25 mm is to be of metal which has a specific gravity of 7, and the remainder of material which has a specific gravity of 0.5. Find the maximum overall length of the cylinder so that it may float in water in stable equilibrium with its axis vertical. 

Answer 1

Question is based on the solid cylinder . Diameter of cylinder, axial length and specific gravity of material are given in the question . Maximum overall length of cylinder has to be determine.

Diameter of cylinder (D) = 0.25 m   

Specific gravity of metal (G_m) = 7

Specific gravity of fluid (G) = 0.5

For floating to happen $W=F_B \implies G_M*A*H=G_{water}*A*l$

$0.5*H=l$

For stable equilibrium $M.G= \frac{l_{min}}{V}=B.G$

So, $\frac{\frac{\pi*254^4}{64}}{\frac{\pi}{4}*250^2*l}=l-0.5 \implies \frac{60.96}{l}=0.5l$

$l=0.044 m$