A ball falls through a liquid at a constant speed. It is acted upon by three forces: an upthrust, a drag-force and its weight.

Question 29

A ball falls through a liquid at a constant speed. It is acted upon by three forces: an upthrust, a drag-force and its weight.

Which statement is correct?

A The drag-force increases with increasing depth.

B The drag-force is equal to the sum of the upthrust and weight.

C The upthrust is constant with increasing depth.

D The weight is greater than the sum of the drag-force and the upthrust.

Reference: Past Exam Paper – March 2019 Paper 12 Q11

Solution:

Answer: C.

The forces acting on the ball falling through the liquid are: upthrust, drag-force and weight.

Upward forces: upthurst and drag-force

Downward force: weight

Since the ball is falling at constant speed, there is no acceleration and thus, the resultant force is zero. The sum of upward forces is equal to the downward force.

Weight = Upthrust + Drag                  [B and D incorrect]

Note that all the three forces remain constant as the ball falls.

Weight = mg               since m and g are constant

The upthrust depends on the pressure difference in the liquid between the top and bottom of the ball (pressure difference = ρgh, where h is the height (diameter) of the ball). Since the diameter of the ball is constant, the upthrust is also constant. [C is correct]

The drag force (a type of friction) depends on the speed of the ball. Since the speed is constant, the drag is also constant. [A incorrect]