A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half subme

Question

A hollow sphere of inner radius 8.0 cm and outer radius 9.0 cm floats half submerged in a liquid of density 8oo kg/m3 .The mass of the sphere is:

(a) 2.1 kg                     (b) .95 kg                     (c) 1.5 kg        (d) 1.2 kg

How much work is done by pressure of forcing 1.4 m3of water through a pipe having an internal diameter of 13 mm if the difference in pressure at the two ends of the pipe is 1.0 atm?

(a) 2.1x105J                (b) 1.4x105J                (c) 1.1x105J                (d) 0.85x105 J

Explanation / Answer

Here ,

let the mass of sphere is m

density of liquid , p = 800 Kg/m^3

when the sphere is half submerged ,

using archimedes principle

(4/3) * pi * 0.09^3 * 800 * 0.5 * g = m * g

solving for m

m = 1.2 kg

the mass of sphere is d) 1.2 kg

------------------------------

pressure , P = 1 atm

P = 1.01 *10^5 Pa

volume , V = 1.4 m^3

work done = P * V

work done = 1.4 * 1.01 *10^5

work done = 1.4 *10^5 J

the work done by the water is b) 1.4 *10^5 J

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