Question

An object of weight $W$ has a uniform rectangular cross section of $a\times 2a$ and density of $0.25gc{m}^{-3}$ . 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. $2\sqrt{2}aW$
• B. $\frac{aW}{\sqrt{2}}$
• C. $\frac{aW}{2}$
• D. $\frac{aW}{2\sqrt{2}}$

Answer 1

Answer: (D)

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