Question

A man is rowing a boat with a constant velocity $v_0$ in a river. The contact area of boat with water is $A$, coefficient of viscosity of water is $\eta$ and the depth of river is $D$. The force required to row the boat is given by,

• A. $\frac{\eta A{v}_0}{D}$
• B. $\frac{\eta A{v}_0}{2D}$
• C. $\frac{A{v}_0}{\eta D}$
• D. $\frac{2\eta A{v}_0}{D}$

Answer 1

The correct option is A $\frac{\eta A{v}_0}{D}$

$F\to$ Force required to row the boat
$F_v\to$ Viscous force on the base of boat

As the boat moves with constant velocity, $F_{net}=0\Rightarrow |{\overrightarrow{F}}_v|=|\overrightarrow{F}|$


Here, $F_v=\eta A\frac{dv}{dz}$

Now, $\frac{dv}{dz}=\frac{v_0-0}{D}=\frac{v_0}{D}$

$\therefore F=F_v=\frac{\eta A{v}_0}{D}$

Hence, $\left(A\right)$ is the correct answer.