A tube of length L is filled completely with an incomeressible liquid of mass M and closed at both the ends. The tube is then rotated 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. `(1)/(2)Momega^(2)L^(2)`
B. `Momega^(2)L`
C. `(1)/(4)Momega^(2)L`
D. `(1)/(2)Momega^(2)L`

Answer

D

Explanation

`dm=(M)/(L)dx`
` dF=dmomega^(2)x`
`F=(M)/(L)omega^(2)int_(0)^(L)xdx=(M)/(L)omega^(2)|(x^(2))/(2)|_(0)^(L)`
`=(1)/(2)Momega^(2)L`