Question

A sphere of radius r is moving at as speed V through air of destiny P. The resistance of force F acting on the sphere is given by the expression. F=Br² PVᵏ where B and k are constant. Use the base unit to determine the value of K​.

Answer 1

The exponent k in the resistance force equation for a sphere moving through air is determined to be 2, based on unit analysis.

Step-by-step explanation:

The value of the exponent k in the drag force equation F = Br² Pvk can be determined by analyzing the units of each component and ensuring that both sides of the equation have the same units. Force has the unit of newtons (N) in the International System of Units (SI). To match these units, the velocity term v must be raised to the second power since the radius r (in meters) squared times the air density P (in kilograms per cubic meter) already has the unit of kilograms times meters, which is a part of the newton's units. Thus, when velocity v (in meters per second) is squared, the resulting units are kilograms times meters squared per second squared, which are equivalent to newtons, confirming that k must have a value of 2.