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A solid cylinder of total length 20 cm floats vertically in a liquid of density 1200 kg/m ^3 . If the length of the cylinder exposed above the liquid surface is 4 cm , the density of the material of the cylinder is:

Options

  1. A240 kg/m ^3
  2. B960 kg/m ^3
  3. C1500 kg/m ^3
  4. D6000 kg/m ^3

Correct answer

B. 960 kg/m ^3

Step-by-step solution

Let the total length of the cylinder be L = 20 cm and the exposed length be h_e = 4 cm . The submerged length of the cylinder is h_s = L - h_e = 20 - 4 = 16 cm . For a floating body in equilibrium, the weight of the body is equal to the buoyant force: _c A L g = _l A h_s g where _c is the density of the cylinder, _l is the density of the liquid, and A is the cross-sectional area. Solving for _c : _c = _l h_s L _c = 1200 16 20 = 1200 0.8 = 960 kg/m ^3 . Answer: 960 kg/m ^3

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