Two copper vessels $A$ and $B$ have the same base area but of different shapes. $A$ takes twice the volume of water as that $B$ requires to fill upto a particular common height. Then the correct statement among the following is
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Pressure depends on height above base only which is same for two vessels.
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The velocity of upper layer of water in a river is $36 kmh ^{-1}$. Shearing stress between horizontal layers of water is $10^{-3} Nm ^{-2}$. Depth of the river is $m$. (Co-efficiency of viscosity of water is $10^{-2} \,Pa . s$ )
A liquid is kept in a cylindrical vessel which rotated along its axis. The liquid rises at the sides. If the radius of the vessel is $0.05\,m$ and the speed of rotation is $2\,rev/s$ , The difference in the height of the liquid at the centre of the vessel and its sides will be .............. $\mathrm{cm}$ $(\pi ^2 = 10)$
A spherical ball of density $\rho$ and radius $0.003$ $m$ is dropped into a tube containing a viscous fluid filled up to the $0$ $ cm$ mark as shown in the figure. Viscosity of the fluid $=$ $1.260$ $N.m^{-2}$ and its density $\rho_L=\rho/2$ $=$ $1260$ $kg.m^{-3}$. Assume the ball reaches a terminal speed by the $10$ $cm$ mark. The time taken by the ball to traverse the distance between the $10$ $cm$ and $20$ $cm$ mark is
( $g$ $ =$ acceleration due to gravity $= 10$ $ ms^{^{-2}} )$
Figure here shows the vertical cross section of a vessel filled with a liquid of density $\rho$. The normal thrust per unit area on the walls of the vessel at the point $P$, as shown, will be
The height of a mercury barometer is $ 75 cm$ at sea level and $ 50 cm$ at the top of a hill. Ratio of density of mercury to that of air is $10^4$. The height of the hill is ....... $km$
A liquid is flowing in a horizontal uniform capillary tube under a constant pressure difference $P$. The value of pressure for which the rate of flow of the liquid is doubled when the radius and length both are doubled is
Toricelli’s barometer used mercury. Pascal duplicated it using French wine of density $984 \;kg m^{-3}$. Determine the height (in $m$) of the wine column for normal atmospheric pressure.
A wooden cube just floats inside water with a $200 \,gm$ mass placed on it. When the mass is removed, the cube floats with its top surface $2 \,cm$ above the water level. the side of the cube is ......... $cm$
A ball of radius $r $ and density $\rho$ falls freely under gravity through a distance $h$ before entering water. Velocity of ball does not change even on entering water. If viscosity of water is $\eta$, the value of $h$ is given by