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Two boats of base areas $A_{1}$ and $A_{2}$ , connected by a string are being pulled by an external force $F_{0}$ . The viscosity of water is n and depth of the water body is H. When the system attains a constant speed, the tension in the thread will be

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$F_{0} \frac{A_{2}}{(A_{1} + A_{2})}$

$F_{0} \frac{A_{1}}{(A_{1} + A_{2})}$

$F_{0} (\frac{A_{2}}{A_{1}})$

$F_{0} (\frac{A_{1}}{A_{2}})$

answer is C.

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Detailed Solution

Viscous force $F \propto$ (area)

So,

F=k A

and

$F_{0} = k (A_{1} + A_{2})$

$T = {kA}_{1}$

Dividing Eq. (ii) by Eq. (i), we get

$\frac{T}{F_{0}} = \frac{A_{1}}{A_{1} + A_{2}} T = \frac{F_{0} A_{1}}{A_{1} + A_{2}}$

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