Two boats of base areas `A_(1)` and `A_(2)`, connected by a string are being pulled by an extermal force `F_(0)`. The velosity is `eta` and depth of the water body is H. when the system attains a constant speed. The tension in the trhead will be

Options

A. `F_(0)(A_(1)/(A_(2)))`
B. `F_(0)(A_(2))/((A_(1)+A_(2)))`
C. `F_(0)(A_(1))/((A_(1)+A_(2)))`
D. `F_(0)(A_(2)/(A_(1)))`

Answer

C

Explanation

Viscous force `Fprop (area)`
So let `F=kA`
`F_(0)=k(A_(1)+A_(2))` …(i)
and `T=k A_(1)` ….(ii)
Divinding Eq, (ii) by Eq. (i) we get,
`(T)/(F_0)=(A_1)/(A_(1)+A_(2))`
`:. T=(F_(0)A_(1))/(A_(1)+A_(2))`.