A wooden plank is floating on the water in a pool. It is tethered to the bottom of the pool by a string attached at mid point of an edge of bottom face, which causes it to float with the diagonal of i

Question

A wooden plank is floating on the water in a pool. It is tethered to the bottom of the pool by a string attached at mid point of an edge of bottom face, which causes it to float with the diagonal of its vertical cross-section coinciding with the level surface of the water, as shown in the figure. What is the specific gravity of the wood?

TestHub · Accepted Answer

With the diagonal of the cross-section on the waterline, half the plank is submerged: $F_{B} = \frac{1}{2} ρ V g$ and string tension $T = F_{B} - W = (\frac{1}{2} - σ) ρ V g$ .

Buoyancy acts at the centroid of the submerged triangular part, weight at the plank's centre, tension at the midpoint of the bottom edge.

Torque balance about the tether point gives $σ = \frac{1}{3}$ - (C)

Physics - Fluid Question with Solution | TestHub

Options:

Doubts & Discussion