A vertical cylindrical container 10 m high and 6 m in diameter is half full of water. Find, to 4 significant figures, the amount of work done in pumping all the water out at the top of the container given that the density of water is 1,000 kg/m³. A) 1.022 × 10⁷ N . m B) 1.10 × 10⁷ N . m C) 1.045 × 10⁷ N . m D) 1.039 × 10⁷ N . m E) 1.323 × 10⁷ N . m

Question

Quizplus · Accepted Answer

The work done in pumping the water out is equal to the potential energy of the water at the top of the container. The potential energy is given by:$$PE = mgh$$where:* m is the mass of the water* g is the acceleration due to gravity* h is the height of the waterThe mass of the water is:$$m = ho V$$where:* ρ is the density of the water* V is the volume of the waterThe volume of the water is:$$V = \frac{1}{2}\pi r^2 h$$where:* r is the radius of the containerSubstituting these expressions into the equation for potential energy, we get:$$PE = \frac{1}{2} ho \pi r^2 h^2 g$$Plugging in the given values, we get:$$PE = \frac{1}{2}(1000 ext{ kg/m}^3)\pi (3 ext{ m})^2 (10 ext{ m})^2 (9.81 ext{ m/s}^2) = 1.039 imes 10^7 ext{ N . m}$$Therefore, the correct answer is D) 1.039 × 10⁷ N . m.

A Vertical Cylindrical Container 10 M High and 6 M