A flat plate of area $10\,cm^2$ is separated from a large plate by a layer of glycerine $1\, mm$ thick. If the coefficient of viscosity of glycerine is $20$ poise, the force required to keep the plate moving with a velocity of $1\,cm/sec$ is .......... $dyne$
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The total area of cross-section is $0.25\,m^2$. If the blood is flowing at the rate of $100\, cm^3/sec$, then the average velocity of flow of blood through the capillaries is ........ $mm/sec$
An object with uniform density $\rho$ is attached to a spring that is known to stretch linearly with applied force as shown below.When the spring object system is immersed in a liquid of density $\rho_1$ as shown in the above figure, the spring stretches by an amount $x_1\left(\rho > \rho_1\right)$. When the experiment is repeated in a liquid of density $\left(\rho_2 < \rho_1\right)$, the spring stretches by an amount $x_2$. Neglecting any buoyant force on the spring, the density of the object is
A tiny spherical oil drop carrying a net charge $q$ is balanced in still air with a vertical uniform electric field of strength $\frac{81 \pi}{7} \times 10^5 \mathrm{Vm}^{-1}$. When the field is switched off, the drop is observed to fall with terminal velocity $2 \times 10^{-3} \mathrm{~ms}^{-1}$. Given $\mathrm{g}=9.8 \mathrm{~ms}^{-2}$, viscosity of the air $=1.8 \times 10^{-5} \mathrm{Ns} \mathrm{m}^{-2}$ and the density of oil $=$ $900 \mathrm{~kg} \mathrm{~m}^{-3}$, the magnitude of $\mathrm{q}$ is
A river gradually deepens, from a depth of $4 \ m$ to a depth of $8\ m$ as shown. The width, $W$, of the river does not change. At the depth of $4 \ m$, the river's speed is $12\ m/sec.$ Its elocity at the $8\ m$ depth is ......... $m/sec$
Water containing air bubbles flows without turbulence through a horizontal pipe which has a region of narrow cross-section. In this region, the bubbles
A barometer kept in an elevator reads $76 \,cm$ when the elevator is accelerating upwards. The most likely pressure inside the elevator (in $cm$ of $Hg$ ) is ........
Two cubical blocks identical in dimensions float in water in such a way that $1^{st}$ block floats with half part immersed in water and second block floats with $3 / 4$ of its volume inside the water. The ratio of densities of blocks is $..........$
Two solids $A$ and $ B$ float in water. It is observed that $A$ floats with $\frac{1}{2}$ of its body immersed in water and $ B$ floats with $\frac{1}{4}$ of its volume above the water level. The ratio of the density of $ A$ to that of $B$ is
A tank with a small hole at the bottom has been filled with water and kerosene (specific gravity $0.8$). The height of water is $3\,m$ and that of kerosene $2\,m$. When the hole is opened the velocity of fluid coming out from it is nearly ........ $ms^{-1}$ .(take $g\, = 10\, m s^{-2}$ and density of water $= 10^3\, kg\, m^{-3}$)
In Guericke's experiment to show the effect of atmospheric pressure, two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the sphere was pumped out to create vacuum inside. If the radius of each hemisphere is $R$ and the atmospheric pressure is $p$, then the minimum force required (when the two hemispheres are pulled apart by the same force) to separate the hemispheres is