A thin square plate of side $2\ m$ is moving at the interface of two very viscous liquids of viscosities ${\eta _1} = 1$ poise and ${\eta _2} = 4$ poise respectively as shown in the figure. Assume a linear velocity distribution in each fluid. The liquids are contained between two fixed plates. $h_1 + h_2 = 3\ m$ . A force $F$ is required to move the square plate with uniform velocity $10\ m/s$ horizontally then the value of minimum applied force will be ........ $N$
$6$
$12$
$24$
$40$
Water flows through a frictionless duct with a cross-section varying as shown in fig. Pressure $p$ at points along the axis is represented by
What is the velocity $v$ of a metallic ball of radius $r$ falling in a tank of liquid at the instant when its acceleration is one-half that of a freely falling body ? (The densities of metal and of liquid are $\rho$ and $\sigma$ respectively, and the viscosity of the liquid is $\eta$).
Why is dust particles settled down on floor in a closed room ? Explain.
A spherical ball of radius $1 \times 10^{-4} \mathrm{~m}$ and density $10^5$ $\mathrm{kg} / \mathrm{m}^3$ falls freely under gravity through a distance $h$ before entering a tank of water, If after entering in water the velocity of the ball does not change, then the value of $h$ is approximately:
(The coefficient of viscosity of water is $9.8 \times 10^{-6}$ $\left.\mathrm{N} \mathrm{s} / \mathrm{m}^2\right)$
There is a $1\, mm$ thick layer of glycerine between a flat plate of area $100\, cm^2$ and a big plate. If the coefficient of viscosity of glycerine is $1.0\, kg\, (m-s)$, then ....... $N$ force is required to move the plate with a velocity of $7\, cm/s$ .