First slide

Fluid statics

Question

A liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis. The liquid rises at its sides. The radius of the vessel is 0.05 m and the speed of rotation is 2 revolutions per second. The difference in the heights of the liquid at the centre and at the sides of the vessel will be (take g = 10 ${ms}^{- 2}$ and $π^{2} = 10$ )

Easy

A

2 cm
B

4 cm
C

1 cm
D

8 cm

Solution

$h = \frac{v^{2}}{2 g} = \frac{r^{2} w^{2}}{2 g} = \frac{{(0.05 \times 4 π)}^{2}}{2 \times 10} = \frac{25 \times 10^{- 4} \times 16 \times π^{2}}{2 \times 10} = 200 \times 10^{- 4} m = 2 cm w = 4 π rad / \sec$

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