The vessel shown in the figure has two sections. The lower part is a rectangular vessel with area of cross-section $A$ and height $h$. The upper part is a conical vessel of height $h$ with base area $‘A’$ and top area $‘a’$ and the walls of the vessel are inclined at an angle $30^o$ with the vertical.A liquid of density $\rho$ fills both the sections upto a height $2h$. Neglecting atmospheric pressure.
AThe force $F $ exerted by the liquid on the base of the vessel is $2h\rho g$$\frac{{(A + a)}}{2}$
Bthe pressure $P $ at the base of the vessel is $2h\rho g $$\frac{A}{a}$
Cthe weight of the liquid $W $ is greater than the force exerted by the liquid on the base
Dthe walls of the vessel exert a downward force $(F-W)$ on the liquid.
Diffcult
Download our app for free and get started
Dthe walls of the vessel exert a downward force $(F-W)$ on the liquid.
d $F=\rho g 2 h A$
Pressure at bottom is $P=\rho g 2 h$
Weight of liquid is $W=\rho g(2 A h-(A-a) h / 2)=\rho g(3 A h / 2+a h / 2)$
We can clearly see $F>W$
Downward forces due to wall is excess forces apart from weight $=F-W$
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 vessels $A$ and $B$ have the same base area and contain water to the same height, but the mass of water in $A$ is four times that in $B$. The ratio of the liquid thrust at the base of $A$ to that at the base of $B$ is
A liquid is kept in a cylindrical vessel. When the vessel is rotated about its axis, the liquid rises at its sides. If the radius of the vessel is $0.05\,\, m$ and the speed of rotation is $2$ revolutions per second, the difference in the heights of the liquid at the centre and at the sides of the vessels will be ...... $cm.$ $($ take $g = 10\,\, ms^{-2}$ and $\pi^2 = 10)$
A dumbbell is placed in water of density $\rho$ . It is observed that by attaching a mass $m$ to the rod, the dumbbell floats with the rod horizontal on the surface of water and each sphere exactly half submerged as shown in the figure. The volume of the mass $m$ is negligible. The value of length $l$ is
In an experiment, a small steel ball falls through a Iiquid at a constant speed of $10\, cm/s$. If the steel ball is pulled upward with a force equal to twice its effective weight, how fast will it move upward ? ......... $cm/s$
Figure shows a container filled with a liquid of density $\rho$. Four points $A, B, C$ and $D$ lie on the diametrically opposite points of a circle as shown. Points $A$ and $C$ lie on vertical line and points $B$ and $D$ lie on horizontal line. The incorrect statement is $\left(p_A, p_B, p_C, p_D\right.$ are absolute pressure at the respective points)
A vessel containing water is moving with a constant speed towards right along a straight horizontal path. if the vessel is given a constant retardation towards the right along a straight line, which of the above diagram represents the surface of the liquid?
A silver ingot weighing $2.1 kg$ is held by a string so as to be completely immersed in a liquid of relative density $0.8$. The relative density of silver is $10.5$ . The tension in the string in $kg-wt$ is
The volume of an air bubble is doubled as it rises from the bottom of lake to its surface. The atmospheric pressure is $75 \,cm$ of mercury. The ratio of density of mercury to that of lake water is $\frac{40}{3}$. The depth of the lake in metre is .........