A space $2.5\ cm$ wide between two large plane surfaces is filled with oil. Force required to drag very thin plate of area $0.5\ m^2$ just midway the surfaces at a speed of $0.5\ m/sec$ is $1\ N$ The coefficient of viscosity in $kg-s/m^2$ is :
Diffcult
Download our app for free and get started
Velocity gradient $=\frac{0.5}{\frac{2.5}{2} \times 10^{-2}}$
as force on the plate due to viscosity is from upper as well as lower portion of the oil, equal from each part,
Then, $\mathrm{F}=2 \eta \mathrm{A} \frac{\mathrm{dv}}{\mathrm{dz}}=2 \times \eta \times(0.5) \frac{0.5}{1.25 \times 10^{-2}}$
$\Rightarrow \eta=2.5 \times 10^{-2} \mathrm{kg}-\mathrm{sec} / \mathrm{m}^{2}$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A vertical $U-$ tube of uniform inner cross section contains mercury in both sides of its arms. A glycerin (density = $1.3 g/cm^3$) column of length $10 $ $cm $ is introduced into one of its arms. Oil of density $0.8 gm/cm^3$ is poured into the other arm until the upper surfaces of the oil and glycerin are in the same horizontal level. Find the length of the oil column ........ $cm$. Density of mercury = $13.6 g/cm^3$View Solution
- 2Three identical vessels are filled to the same height with three different liquids $A, B$ and $C$ $({\rho _A} > {\rho _B} > {\rho _C})$. The pressure at the base will beView Solution
- 3A spherical marble of radius $1\, cm$ is stuck in a circular hole of radius slightly smaller than its own radius (for calculation purpose, both can be taken same) at the bottom of a bucket of height $40 \,cm$ and filled with water up to $10 \,cm$. If the mass of the marble is $20 \,g$, then the net force on the marble due to water is close toView Solution
- 4View SolutionA wooden piece floats half submerged in a tub of water. If the system is transferred to a lift ascending with acceleration the wooden piece will
- 5A cylinder containing water, stands on a table of height $H$. A small hole is punched in the side of cylinder at its base. The stream of water strikes the ground at a horizontal distance $R$ from the table. Then the depth of water in the cylinder is ............View Solution
- 6The shown $H$ shaped apparatus contains an ideal incompressible liquid and has dimension as shown in figure . The diameters of the Tubes are small as compared to $h$ and $R$. The apparatus is rotated with a constant angular velocity $\omega$ about a symmetric vertical axis as shown in figure. The pressure at point $A$ isView Solution
- 7A hollow sphere of radius $R$ is filled completely with an ideal liquid of density $\rho$. sphere is moving horizontally with an acceleration $2g,$ where $g$ is acceleration due to gravity in the space. If minimum pressure of liquid is $P_0$, then pressure at the centre of sphere isView Solution
- 8A uniformly tapering vessel is filled with a liquid of density $900 kg/m^3.$ The force that acts on the base of the vessel due to the liquid is ......... $N$. $(g = 10\,m{s^{ - 2}})$View Solution
- 9A given shaped glass tube having uniform cross section is filled with water and is mounted on a rotatable shaft as shown in figure. If the tube is rotated with a constant angular velocity $\omega $thenView Solution
- 10Two immiscible liquids $A$ and $B$ are kept in an U-tube. If the density of liquid $A$ is smaller than the density of liquid $B$, then the equilibrium situation isView Solution