Example $3$:

A rectangular steel plate $0,5mx0,5m,$ is hanging vertically

from a hinge fixed to the top horizontal edge. The mass of the

plate is $12$ kg $.$ A jet of water strikes the plate in the centre.

The jet velocity is $10\frac{m}{s}$ and the diameter $25$ mm $.$

$($a$)$ Calculate the torque required from a coil spring at the

hinge to keep the plate vertically.

$($b$)$ If the jet velocity is increased to $15\frac{m}{s}$ and the torque

remains the same, determine the angle through which the

plate is deflected to its new position of equilibrium.