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 (a) `( b ) (c) (d)(( e ) dy)/( f )(( g ) dt)( h ) (i)+K=0( j )` (k) (b) `( l ) (m) (n)(( o ) d r)/( p )(( q ) dt)( r ) (s)-K=0( t )` (u) (c) `( d ) (e) (f)(( g ) d r)/( h )(( i ) dt)( j ) (k)=K r (l)` (m) (d) None of these

Options

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

Answer

A

Explanation

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