91Ó°ÊÓ

An item falling through a fluid at its greatest speed is said to have reached its terminal velocity. When the combined drag and buoyancy forces are equal to the force of gravity pulling the item downward, it is seen. Since there is no net force exerted on the object, there is no acceleration of the object.

The gravity acts in the same proportion on both tennis balls for negligible air resistance so both tennis ball will fall at the same speed and strikes the ground simultaneously with the same duration to reach the ground.

The air resistance causes drag force on falling tennis balls which varies with the speed of the tennis ball and it is given by the following expression:

${\mathrm{v}}_{\mathrm{t}}=\sqrt{\frac{\mathrm{mg}}{\mathrm{D}}}$

Here, ${\mathrm{v}}_{\mathrm{t}}$is the terminal speed, g is the acceleration due to gravity, D is the drag force, and m is the mass of the ball.

The drag force also varies with the shape and size of the object.

Both tennis balls are identical so the same drag force will act on both balls. The terminal speed of the ball varies with mass and drag force.

As the drag force on both balls is the same but the tennis ball filled with water will fall faster than the empty tennis ball because of more mass so the higher terminal speed. The water-filled tennis ball will take less time to strike the ground than another tennis ball.