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
A$\frac{5}{4}d$
B$\frac{4}{5}d$
C$d$
D$\frac{d}{5}$
IIT 1995, Diffcult
Download our app for free and get started
A$\frac{5}{4}d$
a (a)Weight of cylinder = upthrust due to both liquids
$V \times D \times g = \left( {\frac{A}{5}\, \times \frac{3}{4}L} \right) \times d \times g + \left( {\frac{A}{5} \times \frac{L}{4}} \right) \times 2d \times g$
==>$\left( {\frac{A}{5} \times L} \right)\, \times D \times g = \frac{{A \times L \times d \times g}}{4}$==>$\frac{D}{5} = \frac{d}{4}$ $\therefore \;D = \frac{5}{4}d$
Download our app
and get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
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
A horizontal pipe line carries water in a streamline flow.At a point along the tube where the cross-sectional area is $10^{-2}$ $m^2$, the water velocity is $2$ $ms^{^{-1}}$ and the pressure is $8000 $ $Pa$. The pressure of water at another point where the cross-sectional area is $0.5$ $\times 10^{-2}$ $m^2$ is ........ $Pa$
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 $\mathrm{g}=10 \mathrm{~ms}^{-2}$ )
An $ L-$ shaped glass tube is just immersed in flowing water such that its opening is pointing against flowing water. If the speed of water current is $v$, then
There are two identical small holes of area of cross-section a on the opposite sides of a tank containing a liquid of density $\rho$. The difference in height between the holes is $h$. Tank is resting on a smooth horizontal surface. Horizontal force which will have to be applied on the tank to keep it in equilibrium is
In a $U-$tube as shown in figure, water and oil are in the left side and right side of the tube respectively. The helghts from the bottom for water and oil columns are $15\; \mathrm{cm}$ and $20\; \mathrm{cm}$ respectively. The density of the oil is......$kg/{m}^{3}$
A cork is submerged in water by a spring attached to the bottom of a bowl. When the bowl is kept in an elevator moving with acceleration downwards, the length of spring
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.