A sniper fires a rifle bullet into a gasoline tank making a hole $53.0 m$ below the surface of gasoline. The tank was sealed at $3.10 atm$. The stored gasoline has a density of $660 kgm^{-3}$. The velocity with which gasoline begins to shoot out of the hole is........ $ms^{-1}$
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A vertical triangular plate $ABC$ is placed inside water with side $BC$ parallel to water surface as shown. The force on one surface of plate by water is (density of water is $\rho $ and atmospheric pressure $P_0$ )
A cylindrical vessel of base radius $R$ and height $H$ has a narrow neck of height $h$ and radius $r$ at one end (see figure). The vessel is filled with water (density $\rho_w$ ) and its neck is filled with immiscible oil (density $\rho_0$ ). Then, the pressure at
A plane is in level flight at constant speed and each of its two wings has an area of $40 \mathrm{~m}^2$. If the speed of the air is $180 \mathrm{~km} / \mathrm{h}$ over the lower wing surface and $252 \mathrm{~km} / \mathrm{h}$ over the upper wing surface, the mass of the plane is______ $\mathrm{kg}$. (Take air density to be $1 \mathrm{~kg} \mathrm{~m}^{-3}$ and $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
A homogeneous solid cylinder of length $L$$(L < H/2)$. Cross-sectional area $A/5$ is immersed such that it floats with its axis vertical at the liquid-liquid interface with length $L/4$ in the denser liquid as shown in the fig. The lower density liquid is open to atmosphere having pressure ${P_0}$. Then density $D$ of solid is given by
The limbs of a $U$ -tube glass are lowered into vessels $A$ and $B, A$ containing water. Some air is pumped out through the top of the tube $C$. The liquids in the left hand limb $A$ and the right hand limb $B$ rise to heights of $10\, cm$ and $12\, cm$ respectively. The density of liquid $B$ is ........ $g/cm^3$
The reading of a spring balance when a block is suspended from it in air is $60 \,N$. This reading is changed to $40 \,N$ when the block is submerged in water. The specific gravity of the block must be therefore ............
A leak proof cylinder of length $1 \;\mathrm{m},$ made of a metal which has very low coefficient of expansion is floating vertically in water at $0^{\circ} \mathrm{C}$ such that its height above the water surface is $20\; \mathrm{cm} .$ When the temperature of water is increased to $4^{\circ} \mathrm{C},$ the height of the cylinder above the water surface becomes $21 \;\mathrm{cm} .$ The density of water at $\mathrm{T}=4^{\circ} \mathrm{C},$ relative to the density at $\mathrm{T}=0^{\circ} \mathrm{C}$ is close to
A sphere is dropped under gravity through a fluid of viscosity $\eta$ . If the average acceleration is half of the initial acceleration, the time to attain the terminal velocity is ($\rho$ = density of sphere ; $r$ = radius)
An open $U$-tube contains mercury. When $13.6 \,cm$ of water is poured into one of the arms of the tube, then the mercury rise in the other arm from its initial level is ....... $cm$