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Physics · Pressure due to a fluid column, Pascal's law and its applications, effect of gravity on fluid pressure

The area of cross section of the wider tube shown in figure is . If the boy stan

The area of cross section of the wider tube shown in figure is \( 900 \mathrm{cm}^{2} \). If the boy standing on the piston weighs 45 kg, the difference in the levels of water in the two tubes.

  • A. \( 50 \mathrm{cm} \)
  • B. 25cm
  • C. \( 75 \mathrm{cm} \)
  • D. 100 \( \mathrm{cm} \)

Step-by-step solution

Using Pascal's law, the pressure exerted by the boy's weight on the piston equals the pressure due to the water column difference. Pressure = Weight/Area = (45 kg × 9.8 m/s²) / (900 cm²). Converting to consistent units: Weight = 45 × 9.8 = 441 N, Area = 0.09 m², so Pressure = 441/0.09 = 4900 Pa. Water pressure = ρgh = 1000 × 9.8 × h = 9800h. Equating: 4900 = 9800h → h = 0.5 m = 50 cm.
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