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A man is rowing a boat of mass m with a constant velocity $' v_{0}'$ in a river the contact area of boat is 'A' and coefficient of viscosity is $η$ . The depth of river is 'D'. Assume that velocity gradient is constant. The force required to row the boat is

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$\frac{3 {ηAv}_{0}}{2 D}$

$\frac{{ηAv}_{0}}{D}$

$\frac{2 {ηAv}_{0}}{D}$

$\frac{{ηAv}_{0}}{2 D}$

answer is C.

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Detailed Solution

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 $F_{v} = ηA \frac{dv}{dz}, but \frac{dv}{dz} = \frac{v_{0} - 0}{D} = \frac{v_{0}}{D}$

then $F_{ext} = F_{v} = \frac{{ηAv}_{0}}{D}$

density of water = 1g ${cm}^{- 3}$ )

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