Question 158: Properties of Matter

Question

A cylindrical vessel containing a liquid is
rotated about its axis so that the liquid rises at
its sides as shown in the figure. The radius of
vessel is 5 cm and the angular speed of
rotation is $$\omega $$ rad s
–1
. The difference in the
height, h (in cm) of liquid at the centre of
vessel and at the side will be :

Accepted Answer

Applying pressure equation from A to B
P
0
+ $$\rho $$.$${{R{\omega ^2}} \over 2}$$.R - $$\rho $$gh = P
0
$$ \Rightarrow $$ $${{\rho {R^2}{\omega ^2}} \over 2}$$ = $$\rho $$gh
$$ \Rightarrow $$ h = $${{{R^2}{\omega ^2}} \over 2}$$ = $${\left( 5 \right)^2}{{{\omega ^2}} \over {2g}}$$ = $${{25} \over 2}{{{\omega ^2}} \over g}$$

Answer

$${{2{\omega ^2}} \over {25g}}$$

Answer

$${{5{\omega ^2}} \over {2g}}$$

Answer

$${{25{\omega ^2}} \over {2g}}$$

Answer

$${{2{\omega ^2}} \over {5g}}$$

Properties of Matter

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