2.101 Buoyant force on a cylinder

Problem 2.101: A cylinder of radius $R$ is kept embedded along the wall of a container of water of density $\rho$. Length of the cylinder is $L$. Determine the vertical force exerted by water on the cylinder. Solution: The cylinder is completely immersed in water. The...

2.100 Compressibility of a liquid

Problem 2.100: Find the pressure that must be applied to water at atmospheric pressure to reduce its volume by $1\:%$ .Take compressibility of water $=0.5\times 10^{-9} \:Pa^{-1}$. Solution: Compressibility of a liquid is the measure of change in volume under external...

2.97 Thermal expansion of a sphere

Problem 2.97:The radius of a metal sphere at room temperature $T$ is $R$, and the coefficient of linear expansion of the metal is $\alpha$ . The sphere is heated a little by a temperature $\triangle\:T$  so that its new temperature is $T\:+\:\triangle\:T$ . Find the...

2.96 Pressure in a liquid

Problem 2.96: An open container has water to a depth of $2\:m$ and above this an oil of relative density $ 0.9$ for a depth of $1\:m$. Find the pressure at the interface of two liquids. Take density of water $ =\: 10^3\:kg\:m^3$, acceleration due to gravity...

2.95 Capillary rise in two tubes

Problem 2.95: Two narrow tubes of inner diameters $3.0\:mm$ and $6.0\:mm$ are joined together to form U-tube open at both the ends. If the U-tube contains water, what is the difference in its levels in the two limbs of the tube? Take density of water$ =\:...

2.94 Surface tension of a liquid

Problem 2.94: A liquid bubble $2\:cm$ in radius has an internal pressure of $13\:Pa$. Calculate the surface tension of liquid film. Solution: A bubble has two surfaces that come in contact with air. There are molecules on both these surface that produce a tangential...

2.93 Capillary rise of a liquid in a tube

Problem 2.93: Determine the minimum size of the glass tubing that can be used to measure water level if capillary rise is not to exceed $2.5\:mm$. Take density of water$ =\: 10^3\:kg\:m^3$, surface tension of water $=\:0.0736\: N\:m^{-1}$ and acceleration due to...

2.92 Elongation of a wire

Problem 2.92: A circular steel wire 2.00 m long must stretch no more than 0.25 cm when a tensile force of 400 N is applied to each end of the wire. What minimum diameter is required for the wire? Given that Young’s modulus of steel is $2\times 10^{11}\:Nm^{-2}$....

2.91 U-tube in equilibrium

Problem 2.91:A U-tube of uniform cross-sectional area, open to the atmosphere, is partially filled with mercury and water as shown. At equilibrium $h_2\:=\:1.00\: cm$. Determine the value of $h_1$. Take density of mercury as $13.6\times 10^{3}\:kg\:m^{-3}$ and density...

2.90 Pressure difference across a venturi tube

Problem 2.90:A venturi meter with a neck diameter of $7.5\:cm$ is connected to a $15\:cm$ pipe through which water flows at a steady rate. A U-tube manometer connected across it shows a reading of $80\:mm$ of mercury. Determine the pressure difference across the...

2.89 Force to hold a ball under water

Problem 2.89:A solid ball has a radius of $3.0\: cm$  and average density of $0.5\: g\:cm^{-3}$. What force is required to hold it completely submerged under water?Take acceleration due to gravity as $9.8\:ms^{-2}$ density of water as  $1.0\:g\:cm^{-3}$. Solution: The...

2.88 Force at the bottom of a water tank

Problem 2.88: A water tank has dimensions $5.0\: m$ X $5.0 \:m$ and a level bottom. The tank is filled to a depth of $3.00 \:m$ with water. Calculate  the force of water on the bottom surface. Take acceleration due to gravity as $9.8\:ms^{-2}$ density of water as...

2.87 Metal block immersed in water

Problem 2.87:A block made out of aluminum has a mass $2.0 \:kg$.  It is suspended from a string and then completely immersed in a container of water. Calculate the tension in the string after the metal is immersed.Take acceleration due to gravity as $9.8\:ms^{-2}$...

2.86 Submergence of a body in a liquid

Problem 2.86: A block of density $600\:kg\:m^3$ floats in a fluid of density $900\:kg\:m^3$. This is shown in the diagram here. The block has height $45\:cm$ . By what depth $h$ is the block submerged? Solution:   A body can float in a liquid when its weight is...

2.85 Apparent weight of a body in a liquid

Problem 2.85: An iron ball of density $8000\: kgm^{-3}$ appears $200 \:N$ lighter in water than in air. FInd  volume of the anchor. Take density of water as $1000\: kgm^{-3}$ and acceleration due to gravity as $10\:ms^{-2}$. Solution: Think of the iron ball in water....

2.84 Capillary rise of water in glass tube

Problem 2.84:Water rises in a capillary tube to a certain height such that the upward force due to surface tension is balanced by $7.5\times 10^{-4}\: N$ force due to the weight of the liquid.  If the surface tension of water is $6 \times  10^{-2}\: Nm^{-1}$,...

2.83 Surface tension of a liquid

Problem 2.83:A hemi spherical drop of diameter $2\:mm$ hangs on a ceiling as shown in the diagram.Determine the surface tension. Density of the liquid is $0.9\times 10^{3}\:kg m^{-3}$. Acceleration due to gravity $g\:=\:10\:ms^{-2}$. Solution:  The drop has weight. It...

2.82 Speed of flow

Problem 2.82: A shower head with $20$ circular openings, each with radius $1.0 \:mm$ is connected to a pipe with radius $1.0 \:cm$. Water flows in the tube at a speed of $4.0\:cm\:s^{-1}$. What is its speed as it exits the shower-head openings? Solution: Water coming...