In the figure shown, the heavy cylinder (radius R) reasting on a smooth surface separates two liquids of densities `2rho` and `3rho`. The height h for the equilibrium of cylinder must be

(i) In the figure shown, the heavy cylinder (radius R) resting on a smooth surface separates two liquids of densities 2rho and 3rho . Find the height 'h' for the equilibrium of cylinder. (ii) The cross section of a dam wall is an arc of a circle of radius R=20m subtending on angle of theta=60^(@) at the centre of the circle. the centre (O) of the circle lies in the water surface. The width of the dam (i.e., dimension perpendicular to the figure) is b=10m. Neglect atmospheric pressure is following calculations. (a) Calculate the vertical component of force (F_(x)) applied by water on the curved dam wall. (b) Calculate the horizontal component of force (F_(H)) applied by water on the curved dam wall. (c) Calculate the resultant force applied by the water on the curved dam wall.

A cylinder stands vertical in two immiscible liquids of densities rho and 2rho as shown. Find the difference in pressure at point A and B:

The velocity of the liquid coming out of a small hole of a vessel containing two different liquids of densities 2rho and rho as shown in the figure is

The velocity of the liquid coming out of a small hole of a vessel containing two different liquids of densities 2rho and rho as shown in the figure is

The velocity of the liquid coming out of a small hole of a vessel containing two different liquids of densities 2rho and rho as shown in the figure is

A conical portion of radius R and height H is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass is M. It is suspended by a string in a liquid of density rho where it stays vertical . The upper surface of the cylinder is at depth h below the liquid surface . The force on the bottom of the cylinder by the liquid is

A conical portion of radius R and height H is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass is M. It is suspended by a string in a liquid of density rho where it stays vertical . The upper surface of the cylinder is at depth h below the liquid surface . The force on the bottom of the cylinder by the liquid is

A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass is M. It suspended by a string in a liquid of density rho where it stays vertical. The upper surface of cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder bby the liquid is

A hemispherical portion of radius R is removed from the bottom of a cylinder of radius R. The volume of the remaining cylinder is V and its mass M. It is suspended by a string in a liquid of density rho where it stays vertical. The upper surface of the cylinder is at a depth h below the liquid surface. The force on the bottom of the cylinder by the liquid is