An oil of mass density 800 kg/m3 is contained in a vessel. Calculate the height of water required to develop an equivalent hydrostatic pressure as that developed by oil of height 30 m. Take acceleration due to gravity as 9.81 m/sec2

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  1. 24 m
  2. 32 m
  3. 42 m
  4. 23 m

Answer (Detailed Solution Below)

Option 1 : 24 m
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Explanation:

Given:

Mass density of oil: 800 kg/m3

Acceleration due to gravity: 9.81 m/s2

Height of oil: 30 m

Mass density of water: 1000 kg/m3 1000 \, \text{kg/m}^3

Using Pascal's Law: 

Pressure due to oil height Pressure due to water height

\((\rho g h)_{\text{oil}} = (\rho g h)_{\text{water}} \)

\(800 \times 9.81 \times 30 = 1000 \times 9.81 \times h \\ h = 24 \, \text{m} \)

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