A tube of length L is filled completely with an incompressible liquid of mass M and closed at both ends. The tube is then roted in a horizontal plane about one of its ends with a uniform angular velocity `omega` The force exerted by the liquid at the other end is

Options

A. `(ML^(2)omega^(2))/(2)`
B. `(MLomega^(2))/(2)`
C. `(ML^(2)omega)/(2)`
D. `ML omega^(2)`

Answer

B

Explanation

Let small length be dx of mass dm in tube which exerts centrifugal force at other ends. Centrifugal force on small element is

`dF=dmxomega^(2)`
`intdF=int_(x-0)^(x=L)(M)/(L)dx.xomega^(2)`
`F=(M)/(L)omega^(2)int_(x=0)^(x=L)x.dx=(M)/(L)omega^(2)[(L^(2))/(2)]`
`F=(1)/(2)MLomega^(2)`