Explain with the help of Bernoulli’s principle that why does a spinning ball follows a curve path during flight ?

$(i)$ Ball moving without spin :

In above figure, the streamlines around a non-spinning ball moving relative to the fluid.

It is clear that the velocity of fluid (air) above and below the ball at corresponding points is the same resulting in zero pressure difference.

Air therefore, exerts no upward or downward force on the ball.

Ball moving with spin : As a result there is an upward force resulting in a dynamic lift of the wings.

Streamlines for a fluid around a sphere spinning clockwise

In above figure a spinning ball is shown.

A spinning ball drags air along with it.

If surface is rough more air drags.

The crowding of streamlines at above the ball indicates high velocity and low pressure, while the sparse streamlines below the ball indicates low velocity and high pressure.

Thus difference in velocities of air results in the pressure difference between the lower and upper faces and there is a net upward force on the ball.

This dynamic lift due to spinning is called Magnus effect.