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Question

A liquid is kept in a cylindrical vessel which is rotated along its axis. The liquid rises at the sides as shown in figure below. If the radius of the vessel is 0.05 m and the speed of rotation is 2 rad s1, find the difference in the height of the liquid at the centre of the vessel and its sides

A
20 cm
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B
4 cm
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C
2 cm
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D
0.2 cm
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Solution

The correct option is C 2 cm

According to Bernoulli's theorem
ρ=12ρ v2=constant
Near the ends, the velocity of liquid is higher so that pressure is lower as a result the liquid rise at the sides to compensate for this drop of pressure
i.e.,ρ g h=12ρ v2=12ρ r2 w2

Hence,h=r2w22g
=r2(2π v)22g
=2π2r2v2g
=2×π2× (0.05)2× 229.8
= 0.02 m = 2 cm


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