A cylinder of radius $4\ cm$ and height $10\ cm$ is immersed in two liquids as shown. Specific gravity of oil is $0.5$ . $2\ cm$ of cylinder is in the air. Select the $INCORRECT$ statement. Neglect atmospheric pressure.
Force exerted by oil on the cylinder is zero.
Force exerted by water on the cylinder is $0.96\,\pi $ newton.
Force exerted by both water and oil is $1.14\,\pi $ newton.
Frequency of oscillation does not depend on density of oil, if cylinder is displaced slightly.
In the arrangement shown both the vessels $A$ and $B$ are identical but amount of water in $B$ is double of that in $A$. The vessels are closed by identical leak proof pistons at the same height. The pistons are connected to the ends of lever arm. There is no friction between the pistons and the container walls. The system is in equilibrium in the situation shown. Now the valve in the horizontal tube connecting both the vessels is opened. In which direction will the water flow through the tube ?
Two identical cylindrical vessels with their bases at same level each contains a liquid of density $\rho$. The height of the liquid in one vessel is ${h_1}$ and that in the other vessel is ${h_2}$. The area of either base is $A$. The work done by gravity in equalizing the levels when the two vessels are connected, is
In a cylindrical container open to the atmosphere from the top a liquid is filled upto $10\,\, m$ depth. Density of the liquid varies with depth from the surface as $\rho (h) = 100 + 6h^2$ where $h$ is in meter and $\rho$ is in $kg/m^3.$ The pressure at the bottom of the container will be : $($ atmosphere pressure $= 10^5\,\, Pa, \,g = 10\, m/sec^2)$
The two thigh bones (femures), each of cross-sectional area $10 \,cm ^2$ support the upper part of a person of mass $50 \,kg$. The average pressure sustained by the femures is ........... $N / m ^2$
If solid will break under pressure greater than $13\ atm$ and that solid has a specific gravity of $4$ , what is the maximum height of a cylinder made from the solid that can be built at the earth's surface ? (Note: $1\ atm$ = $10^5\ Pa$ .) ......... $m$