A sphere of mass `M` and radius `R` is falling in a viscous fluid. The terminal velocity attained by the falling object will be alphaortional to :

Options

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

Answer

A

Explanation

Stoke's law:`6piretav=(4)/(3)pir^(3)(rho-sigma)g``therefore V oo r^(2)`As M is given,`rho=(M)/((4)/(3)pir^(3))` but as `r^(3)` increases and `rho` is a constant `sigma` also is a constant.
`therefore` v,the terminal velocity `oo r^(2)`