Question

An object of weight $W$ has a uniform rectangular cross section of $a\times 2a$ and density of $0.25gcm^{- 3}$ . Part of it is immersed in water and the rectangle is tilted by $45^{^\circ }$ , while one of its corners is just at the water surface. Calculate the torque of the buoyancy force with respect to center of mass of the object.

• A. $2 \sqrt{2} a W$
• B. $\frac{{aW}}{\sqrt{2}}$
• C. $\frac{{aW}}{2}$
• D. $\frac{a W}{2 \sqrt{2}}$

Answer 1

Answer: (D)

$\mathrm{W}=$ buoyancy force
Consider the center of mass and symmetry of immersed part
of the object.
$r=\frac{1}{4} \sqrt{a^{2}+a^{2}}=\frac{a}{2 \sqrt{2}}$
$\tau=W r=\frac{a W}{2 \sqrt{2}}$