A right circular cylinder has a mass $m$, radius $r$, and a height $h$. The cylinder is completely submerged in a fluid of density $\rho$, as shown in the diagram. What is the magnitude of the net force on the cylinder?
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An inverted tube barometer is kept on a lift with a moving downward with a deceleration $\alpha $ . The density of mercury is $\rho$ and acceleration due to gravity is $g$ . If the atmospheric pressure be $P_0$ then
A liquid having coefficient of viscosity $0.02$ decapoise is filled in a container of cross-sectional area $20 \,m ^2$. If viscous drag between two adjacent layers in flowing is $1 \,N$, then velocity gradient is ........ $s ^{-1}$
There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $d_1$ and $d_2$ are filled in the tube. Each liquid subtends $90^o$ angle at centre. Radius joining their interface makes an angle $\alpha$ with vertical. Ratio $\frac{{{d_1}}}{{{d_2}}}$ is
A Newtonian fluid fills the clearance between a shaft and a sleeve. When a force of $800$ $N$ is applied to the shaft, parallel to the sleeve, the shaft attains a speed of $1.5$ $cm/sec$. If a force of $2.4$ $kN$ is applied instead, the shaft would move with a speed of ......... $ cm/sec$
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 $..........$
A pan balance has a container of water with an overflow spout on the right-hand pan as shown. It is full of water right up to the overflow spout. A container on the left-hand pan is positioned to catch any water that overflows. The entire apparatus is adjusted so that it’s balanced. A brass weight on the end of a string is then lowered into the water, but not allowed to rest on the bottom of the container. What happens next ?
A rectangular block is $10 \,cm \times 10 \,cm \times 15 \,cm$ in size is floating in water with $10 \,cm$ side vertical. If it floats with $15 \,cm$ side vertical, then the level of water will ..........
Two water pipes of diameters $ 2 cm $ and $4 cm $ are connected with the main supply line. The velocity of flow of water in the pipe of $ 2 cm$ diameter is
Air streams horizontally past an air plane. The speed over the top surface is $60 \,m / s$ and that under the bottom surface is $45 \,m / s$. The density of air is $1.293 \,kg / m ^3$, then the difference in pressure is ....... $N / m ^2$