Embibe Experts Solutions for Chapter: Fluid Mechanics, Exercise 2: Exercise - 2

A liquid is kept in a cylindrical vessel which is rotated about its axis. The liquid rises at the sides. If the radius of the vessel is $0.05 \mathrm{m}$ and the speed of rotation is $2 \mathrm{rev} {\mathrm{s}}^{-1}$, The difference in the height of the liquid at the centre of the vessel and its sides will be $\left({\pi }^2=10\right)$

Pressure gradient in a static fluid is represented by $z$-direction is vertically upwards, and $x$-axis is along horizontal, $d$ is density of fluid):

The vessel shown in the figure has two sections of the area of cross-section $A_1$ and $A_2$. A liquid of density $\mathrm{\rho }$ fills both the sections, up to height $h$ in each. Neglecting atmospheric pressure.

A cubical block of wood of edge $10 \mathrm{cm}$ and mass $0.92 \mathrm{kg}$ floats on a tank of water with oil of relative density$0.6.$ Thickness of oil is $4 \mathrm{cm}$ above water. When the block attains equilibrium with four of its sides edges vertical:

Following are some statements about buoyant force, select incorrect statement/statements. (Liquid is of uniform density) 

A wooden block with a coin placed on its top, floats in water as shown in figure. The distance $l$ and $\mathrm{h}$ are shown here. After some time the coin falls into the water. Then :

A block of density$2000 \mathrm{kg} {\mathrm{m}}^{-3 }$and mass $10 \mathrm{kg}$ is suspended by a spring stiffness $100 \mathrm{N} {\mathrm{m}}^{-1}.$ The other end of the spring is attached to a fixed support. The block is completely submerged in a liquid of density $1000 \mathrm{kg} {\mathrm{m}}^{-3}$ If the block is in equilibrium position then,

A cylindrical vessel of$90 \mathrm{cm}$height is kept filled up to the brim as shown in the figure. It has four holes $1, 2, 3, 4$which are respectively at heights of $20 \mathrm{cm}, 30 \mathrm{cm}, 40 \mathrm{cm}$ and $50 \mathrm{cm}$ from the horizontal floor $PQ.$ The water falling at the maximum horizontal distance from the vessel comes from