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Question 1: From the top of a tall building, you drop two table tennis balls, one filled with air and the other with water. Which ball reaches terminal velocity first and why?


The lighter ball, i-e, the one filled with air, will reach its terminal velocity first.

Consider two table tennis balls (this means both have same shape and size). One ball is filled with air and the other with water. When they are dropped in the air (medium is same), a drag force acts on both of them. The drag force is acting upwards as against the force of gravity and gradually increasing with the velocity of the object. A stage reaches when the downwards gravitational force and the upwards drag forces are equal. Then the net force on the object is zero and it is falling with uniform velocity, called terminal velocity. Mathematically, the drag force for spherical objects like a table tennis ball is given by

FD = 6πηrv

Where r is the radius of the sphere (ball in this case) and v is its velocity. η is called viscosity and is the characteristic of the medium in which the body is falling. This is also same for both the balls.

At terminal velocity vT, this drag force (acting upwards) is equal to the gravitational force (i-e, weight). Therefore,

Since g, π, η and r are constants for both balls, therefore, vT is proportional to the masses of the balls. Now the mass of the ball filled with air is less than the mass of the ball filled with water, therefore, the terminal velocity of the air filled ball will also be less. This means that the ball filled with air will take less time to attain its terminal speed as compared to the heavier water filled ball.

Follow up question

Is it possible that two spherical shapes of different radii and different masses are set to fall in the same medium (say air or water) and they attain same terminal speed?

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