Spherical rain drop evaporates at a rate proportional to its surface area. The differential equation corresponding to the rate of change of the radius of the rain drop if the constant of proportionality is `K >0` is

Options

A. `(dr)/(dt)+ K=0`
B. `(dr)/(dt) -K =0`
C. `(dr)/(dt) = Kr`
D. None of these

Explanation

`(dV)/(dt) = -K4pir^(2)`…………..(1)
But `V=4/3pir^(3)`
or `(dV)/(dt) = 4pir^(2)(dr)/(dt)` ……………(2)
Hence, `(dr)/(dt) =-K`