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 .

Explanation

In rotational motion the angular velocity remains same for all points so the force required for the circular motion of element shown in Fig . 7.67.

dF = (dm) x `omega^(2)` [ as F = mr `omega^(2)`]
i.e., dF = `[(M)/(L) dx] xomega^(2) " " [ "as dm" = (M)/(L) dx`]
So , `F = int_(0)^(L)(M//L)omega^(2)x dx = (1//2) M omega^(2)L`