A tube of length L is filled completely with an incompressible 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`. Determine the force exerted by the liquid at the other end.

Options

A. `Momega^(2)L/2`
B. `Momega^(2)L`
C. `Momega^(2)L/4`
D. `Momega^(2)L^(2)/2`

Answer

a

Explanation

Mass of liquid in unit length `=M/L`
`therefore` Mass in element dx= `(Mdx)/L`
`therefore` Centripetal force `=(Mdx)/(L)xomega^(2)`
or `dF = (Momega^(2))/(L) x dx`
`therefore int dF = int_(0)^(L) (Momega^(2))/(L) xdx`
or `F=(Momega^(2))/(L) [x^(2)/2]_(0)^(L) = (ML^(2)omega^(2))/(2L)`or `F = (MLomega^(2))/(2)`.