A man is rowing a boat with a constant velocity `v_(0)` in a river. The contact area of boat is `'A'` and coefficient of viscosity is `eta`. The depth of river is `'D'` . Find the force required to row the boat.

Options

A. `(etaAv_0)/(2D)`
B. `(2etaAv_0)/(D)`
C. `(etaAv_0)/(D)`
D. `(3etaAv_0)/(2D)`

Answer

C

Explanation

We can draw the free body diagram of boat
`F_(ext)=F_v=ma_(res)`
As boat moves with constant velocity `a_(res)=0`
`F_(ext)=F_v`
But `F_V=etaA(dv)/(dz)`, but `(dv)/(dz)=(v_0-0)/(D)=(v_0)/(D)`
then `F_(ext)=F_V=(etaAv_0)/(D)`