A dry clean steel needle of diameter d and density `rho` when carefully placed on the surface of water remains floating . If T is the surface tension of water , then maximum value for the diameter d of the needle for enabling it to float will be

Options

A. `d=sqrt((8 rho pi)/(T g ))`
B. `d=sqrt((4 rho pi)/(T g ))`
C. `d=sqrt((8 T)/(rho pi g ))`
D. data incomplete

Answer

C

Explanation

Force due to surface tension = 2 l T
Force of weight of needle `=pid^2/4xxlxxrhoxxg` Equate the two