Question

Water is flowing in a streamline down a plane having the inclination of ${30}^0$ with the horizontal. A box ABCD attached with the wall is floating on the surface of the water keeping face CD of the box downward as shown in the figure. The box has a weight of 200 N and area of the base is $1m^2$ . If the velocity of the streamline at a distance of 1mm from the base CD is 0.1 m/s. Then the tension in the string connecting the block to the wall as shown is (Given viscosity of water $=0.1\text{N-s}/{\text{m}}^2$)

• A. 110 N
• B. 90 N
• C. 95 N
• D. 100 N

Answer 1

The correct option is A

110 N

Viscous force down the incline can be given as,$\tau =\eta A\frac{dv}{dy}=0.1\times 1{\text{m}}^2\times \frac{{10}^{-1}}{{10}^{-3}}=10\text{N}$

$\therefore \text{T}=\tau +100=110\text{N}$