A solid metallic sphere of radius r is allowed to fall freely through air. If the frictional resistance due to air is proportional to the cross-sectional area and to the square of the velocity, then the terminal velocity of the sphere is proportional to which of the following ?

Options

A. `r^(2)`
B. r
C. `r^(3//2)`
D. `r^(1//2)`

Answer

D

Explanation

At terminal velocity `W=F_(r )`
`(4)/(3)pir^(3)rhog=Kpir^(2)v_(T)^(2)`
`v_(T)propr^(1//2)`