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

Options

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

Answer

A

Explanation

Consider a small mass element dm at distance x from axis
Required force `F=intdf=int(dm)(omega^(2))(x)
int_(0)^(L)(M)/(L)omega^(2)dx=(Momega^(2)L)/(2)`