The amount of work done in pumping water out of a
cubical vessel of height 1 m is nearly
(a) 5000 j
(b) 1 j
(c) 5job
(d) 10 j

(a) 5000 J

Explanation:

For a layer of water dx thick, the volume is:

dV = (1 m²) dx

The density of water is 1000 kg/m³, so the mass of the layer is:

dm = (1000 kg/m³) dV

dm = (1000 kg/m) dx

If the layer is a distance x from the top of the vessel, then the work to lift it is:

dW = dm g x

dW = (1000 kg/m) (10 m/s²) x dx

dW = (10000 N/m) x dx

Integrating from x = 0 m to x = 1 m:

W = ∫ dW

W = 10000 N/m ∫₀¹ x dx

W = 10000 N/m (½ x² |₀¹)

W = 10000 N/m (½ (1 m)² − ½ (0 m)²)

W = 5000 J