An aeroplane of mass $3 \times 10^4\,kg$ and total wing area of $120\,m^2$ is in a level flight at some height. The difference in pressure between the upper and lower surfaces of its wings in kilopascals is........... $kPa$ $(g=10\,m/s^2)$
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In Guericke's experiment to show the effect of atmospheric pressure, two copper hemispheres were tightly fitted to each other to form a hollow sphere and the air from the sphere was pumped out to create vacuum inside. If the radius of each hemisphere is $R$ and the atmospheric pressure is $p$, then the minimum force required (when the two hemispheres are pulled apart by the same force) to separate the hemispheres is
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?
A tall tank filled with water has an irregular shape as shown. The wall $C D$ makes an angle of $45^{\circ}$ with the horizontal, the wall $A B$ is normal to the base $B C$. The lengths $A B$ and $C D$ are much smaller than the height $h$ of water (figure not to scale). Let $p_1, p_2$ and $p_3$ be the pressures exerted by the water on the wall $A B$, base $B C$ and the wall $C D$ respectively. Density of water is $\rho$ and $g$ is acceleration due to gravity. Then, approximately
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)
A uniform cylinder of length $L$ and mass $M$ having crosssectional area $A$ is suspended, with its length vertical, from a fixed point by a massless spring such that it is half submerged in a liquid of density $\sigma$ at equilibrium position. The extension $x_0$ of the spring when it is in equilibrium is
The velocity of a small ball of mass $\mathrm{M}$ and density $d,$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $\frac{\mathrm{d}}{2}$, then the viscous force acting on the ball will be :
A cubical block of wood $10 \,cm$ on a side floats at the interface between oil and water with its lower surface horizontal and $4\, cm$ below the interface. The density of oil is $0.6gc{m^{ - 3}}$. The mass of block is ...... $gm$
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