Question

A uniformly tapering vessel is filled with a liquid of uniform density 900 kg/m³. The force that acts on the base of the vessel due to the liquid is (g = 10 ms⁻²)

• A. 3.6 N
• B. 7.2 N
• C. 9.0 N
• D. 14.4 N

Answer 1

Answer: (B)

7.2 N

Answer 2

The force on the base of the vessel due to the liquid is calculated by multiplying the pressure at the base by the area of the base. The pressure at a depth $h$ in a liquid of density $\rho$ is given by $P = \rho g h$.

Given: Density of liquid, $\rho = 900$ kg/m³ Height of liquid, $h = 0.4$ m Acceleration due to gravity, $g = 10$ m/s² Area of the base, $A_{base} = 2 \times 10^{-3}$ m²

Pressure at the base: $P = \rho g h$ $P = (900 \text{ kg/m³}) \times (10 \text{ m/s²}) \times (0.4 \text{ m})$ $P = 3600 \text{ N/m²}$

Force on the base: $F = P \times A_{base}$ $F = (3600 \text{ N/m²}) \times (2 \times 10^{-3} \text{ m²})$ $F = 7.2 \text{ N}$