Question

A man is rowing a boat with a constant velocity $v_o$ in a river of depth ${}^{\prime }{D}^{\prime }$. The contact area of boat is ${}^{\prime }{A}^{\prime }$ and coefficient of viscosity of water is $\eta$. Find the force required to row the boat.

• A. $\frac{\eta v_o}{D}$
• B. $\frac{\eta A^2{v}_o}{D}$
• C. $\frac{\eta D^2{v}_o}{A}$
• D. $\frac{\eta A{v}_o}{D}$

Answer 1

The correct option is D $\frac{\eta A{v}_o}{D}$



Using Newton's second law,
$F-F_{\tau }=ma$
As the boat moves with constant velocity.
Acceleration, $a_{res}=0$
$\Rightarrow F=F_{\tau }$
But tangential force, $F_{\tau }=\eta A\frac{dv}{dz}$
where $\frac{dv}{dz}=\frac{v_o-0}{D}=\frac{v_o}{D}$
$\Rightarrow F=F_{\tau }=\frac{\eta A{v}_o}{D}$