Exercise 1

For the system shown in the figure, the cylinder on the left at$L$has a mass of $600 \mathrm{kg}$ and cross-sectional area of $800 {\mathrm{cm}}^2$. The piston on the right, at $S$, has cross-sectional area $25 {\mathrm{cm}}^2$ and negligible weight. If the apparatus is filled with oil$\left(\rho =0.75\mathrm{gm} {\mathrm{cm}}^{-3}\right)$. Find the force $F$required to hold the system in equilibrium

Glycerine flows steadily through a horizontal tube of length $1.5 m$ and radius $1.0 cm$. If the amount of glycerine collected per second at one end is$4.0\times {10}^{-3} kg{s}^{-1}$, what is the pressure difference between the two ends of the tube ? (Density of glycerine$=1.3\times {10}^3 kg{m}^{-3}$, and coefficient of viscosity of glycerine $=0.83 Ns{m}^{-2}$)

A cubical vessel of side $3 \mathrm{cm}$ and mass $150 \mathrm{g}$ is filled with $0.75$ litre of a liquid. The vessel with liquid is placed on a table, then pressure exerted on the table by the vessel is _____.

Explain Stokes Law.

A jet of water having velocity$=10 \mathrm{m} {\mathrm{s}}^{-1}$ and stream cross-section$=2 {\mathrm{cm}}^2$ hits a flat plate perpendicularly, with the water splashing out parallel to plate. Find the force that the plate experiences

The area of cross-section of the wider tube shown in figure is $800 {\mathrm{cm}}^2$^​. If a mass of $12 \mathrm{kg}$ is placed on the massless piston, the difference in heights h in the level of water in the two tubes is

The pressure at the bottom of a tank of water is $3\mathrm{P}$ where $\mathrm{P}$ is the atmospheric pressure. If the water is drawn out till the level of water is lowered by one-fifth, the pressure at the bottom of the tank will now be

Calculate the mass of alcohol flowing in two minutes through a tube of radius $5\times {10}^{-4} m$ and length $0.5 m$, if there is a constant pressure head of$0.6 m$  of alcohol. Density of alcohol is $800 \raisebox{1ex}{$kg$}\!\left/ \!\raisebox{-1ex}{$m^3$}\right.$. Coefficient of viscosity of alcohol$=1.38\times {10}^{-3} \raisebox{1ex}{$Ns$}\!\left/ \!\raisebox{-1ex}{$m^3$}\right.$?