Question

A cylinder of radius R is floating in a liquid as shown. The work done in submerging the cylinder completely in the liquid of density r is

• A. $\frac{2}{9}$rpR²L²g
• B. $\frac{8}{18}$rpR²L²g
• C. $\frac{1}{3}$rpR²L²g
• D. $\frac{2}{9}$rR²L²g

Answer 1

Answer: (A)

$\frac{2}{9}$rpR²L²g

Answer 2

At any submerged length x

F_B = rpR²xg ... (1)

If density of cylinder is r_C then, $\frac{\rho_{C}}{\rho}$= $\frac{\frac{L}{3}}{L}$= $\frac{1}{3}$ Ž r_C = $\frac{\rho}{3}$

then, W = $\int_{L/3}^{L}{\left( \rho\pi R^{2}xg - \frac{\rho}{3}\pi R^{2}Lg \right)dx}$