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29 August, 09:13

The amount of work done in pumping water out of a

cubical vessel of height 1 m is nearly

(a) 5000 J

(b) 10000 J

(c) 5Job

(d) 10 J

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Answers (1)
  1. 29 August, 09:36
    0
    (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
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