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A cylindrical vessel filled with water upto height of $H$ stands on a horizontal plane. The side wall of the vessel has a plugged circular hole touching the bottom. The coefficient of friction between the bottom of vessel and plane is $\mu$ and total mass of water plus vessel is $M$. What should be minimum diameter of hole so that the vessel begins to move on the floor if plug is removed (here density of water is $\rho$ )
Two bodies are in equilibrium when suspended in water from the arms of a balance. The mass of one body is $36 g $ and its density is $9 g / cm^3$. If the mass of the other is $48 g$, its density in $g / cm^3$ is
A liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis, the liquid rises at its sides. If the radius of the vessel is $0.05\,\, m$ and the speed of rotation is $2$ revolutions per second, the difference in the heights of the liquid at the centre and at the sides of the vessels will be ...... $cm.$ $($ take $g = 10\,\, ms^{-2}$ and $\pi^2 = 10)$
Two communicating vessels contain mercury. The diameter of one vessel is $n$ times larger than the diameter of the other. A column of water of height $ h$ is poured into the left vessel. The mercury level will rise in the right-hand vessel ($s =$ relative density of mercury and $\rho = $ density of water) by
Fountains usually seen in gardens are generated by a wide pipe with an enclosure at one end having many small holes. Consider one such fountain which is produced by a pipe of internal diameter $2$ $cm$ in which water flows at a rate $3$ $ms^{^{-1}}$. The enclosure has $100$ holes each of diameter $0.05$ $cm$. The velocity of water coming out of the holes ids ( in $ms^{^{-1}}$)
In a test experiment on a model aeroplane in wind tunnel, the flow speeds on the upper and lower surfaces of the wings are $70 \mathrm{~ms}^{-1}$ and $65 \mathrm{~ms}^{-1}$ respectively. If the wing area is $2 \mathrm{~m}^2$ the lift of the wing is__________ $\mathrm{N}$.
(Given density of air $=1.2 \mathrm{~kg} \mathrm{~m}^{-3}$ )
In a cylindrical container open to the atmosphere from the top a liquid is filled upto $10\,\, m$ depth. Density of the liquid varies with depth from the surface as $\rho (h) = 100 + 6h^2$ where $h$ is in meter and $\rho$ is in $kg/m^3.$ The pressure at the bottom of the container will be : $($ atmosphere pressure $= 10^5\,\, Pa, \,g = 10\, m/sec^2)$