A circular cylinder of height 1.20 m having faces of diameter 0.620 m is immersed in water of density 1.00 × 10³ kg/m³ with its axis vertical so that its faces are parallel to the surface of the water. The upper face is 2.50 m below the surface of the water. The net force on this cylinder is observed to be 1120 N downward. Atmospheric pressure is 1.01 × 10⁵ Pa. What net force does the water exert on the lower face of the cylinder? A) 7.40 × 10³ N B) 1.09 × 10⁴ N C) 3.79 × 10⁴ N D) 4.14 × 10⁴ N E) 1.37 × 10⁵ N

Question

Quizplus · Accepted Answer

First, we need to find the volume of the cylinder.
$V = \pi r^2 h = \pi (\frac{0.62}{2})^2 (1.2) \approx 0.44 m^3$
Next, we need to find the weight of the cylinder.
$W = mg = \rho Vg = (1000)(0.44)(9.81) \approx 4300 N$
Since the cylinder is immersed in water, there is a buoyant force acting on it in the upward direction. We can find the buoyant force using Archimedes' principle.
$F_b = \rho_{water} V_{submerged} g = (1000)(0.44)(2.5)(9.81) \approx 4320 N$
The net force on the cylinder is 1120 N downward, so the force from the water on the lower face of the cylinder must be larger than the weight of the cylinder minus the buoyant force. 
$F_{lower} - W + F_b = 1120$
$F_{lower} = W - F_b + 1120$
$F_{lower} = 4300 - 4320 + 1120$
$F_{lower} \approx 4140 N$
Therefore, the best choice is D.

A Circular Cylinder of Height 1