Physical World and Measurement
Units and Measurements
- International System of Units
- Measurement of Length
- Measurement of Mass
- Measurement of Time
- Accuracy, Precision and Least Count of Measuring Instruments
- Errors in Measurements
- Significant Figures
- Dimensions of Physical Quantities
- Dimensional Formulae and Dimensional Equations
- Dimensional Analysis and Its Applications
- Need for Measurement
- Units of Measurement
- Fundamental and Derived Units
- Length, Mass and Time Measurements
- Introduction of Units and Measurements
Motion in a Plane
- Scalars and Vectors
- Multiplication of Vectors by a Real Number or Scalar
- Addition and Subtraction of Vectors - Graphical Method
- Resolution of Vectors
- Vector Addition – Analytical Method
- Motion in a Plane
- Motion in a Plane with Constant Acceleration
- Projectile Motion
- Uniform Circular Motion (UCM)
- General Vectors and Their Notations
- Motion in a Plane - Average Velocity and Instantaneous Velocity
- Rectangular Components
- Scalar (Dot) and Vector (Cross) Product of Vectors
- Relative Velocity in Two Dimensions
- Cases of Uniform Velocity
- Cases of Uniform Acceleration Projectile Motion
- Motion in a Plane - Average Acceleration and Instantaneous Acceleration
- Angular Velocity
- Introduction of Motion in One Dimension
Motion in a Straight Line
- Position, Path Length and Displacement
- Average Velocity and Average Speed
- Instantaneous Velocity and Speed
- Kinematic Equations for Uniformly Accelerated Motion
- Acceleration (Average and Instantaneous)
- Relative Velocity
- Elementary Concept of Differentiation and Integration for Describing Motion
- Uniform and Non-uniform Motion
- Uniformly Accelerated Motion
- Position-time, Velocity-time and Acceleration-time Graphs
- Position - Time Graph
- Relations for Uniformly Accelerated Motion (Graphical Treatment)
- Introduction of Motion in One Dimension
Laws of Motion
- Aristotle’s Fallacy
- The Law of Inertia
- Newton's First Law of Motion
- Newton’s Second Law of Motion
- Newton's Third Law of Motion
- Conservation of Momentum
- Equilibrium of a Particle
- Common Forces in Mechanics
- Circular Motion and Its Characteristics
- Solving Problems in Mechanics
- Static and Kinetic Friction
- Laws of Friction
- Intuitive Concept of Force
- Dynamics of Uniform Circular Motion - Centripetal Force
- Examples of Circular Motion (Vehicle on a Level Circular Road, Vehicle on a Banked Road)
- Lubrication - (Laws of Motion)
- Law of Conservation of Linear Momentum and Its Applications
- Rolling Friction
- Introduction of Motion in One Dimension
Work, Energy and Power
- Introduction of Work, Energy and Power
- Notions of Work and Kinetic Energy: the Work-Energy Theorem
- Kinetic Energy
- Work Done by a Constant Force and a Variable Force
- Concept of Work
- The Concept of Potential Energy
- Conservation of Mechanical Energy
- Potential Energy of a Spring
- Various Forms of Energy : the Law of Conservation of Energy
- Non - Conservative Forces - Motion in a Vertical Circle
Motion of System of Particles and Rigid Body
System of Particles and Rotational Motion
- Motion - Rigid Body
- Centre of Mass
- Motion of Centre of Mass
- Linear Momentum of a System of Particles
- Vector Product of Two Vectors
- Angular Velocity and Its Relation with Linear Velocity
- Torque and Angular Momentum
- Equilibrium of Rigid Body
- Moment of Inertia
- Theorems of Perpendicular and Parallel Axes
- Kinematics of Rotational Motion About a Fixed Axis
- Dynamics of Rotational Motion About a Fixed Axis
- Angular Momentum in Case of Rotation About a Fixed Axis
- Rolling Motion
- Momentum Conservation and Centre of Mass Motion
- Centre of Mass of a Rigid Body
- Centre of Mass of a Uniform Rod
- Rigid Body Rotation
- Equations of Rotational Motion
- Comparison of Linear and Rotational Motions
- Values of Moments of Inertia for Simple Geometrical Objects (No Derivation)
- Kepler’s Laws
- Newton’s Universal Law of Gravitation
- The Gravitational Constant
- Acceleration Due to Gravity of the Earth
- Acceleration Due to Gravity Below and Above the Earth's Surface
- Acceleration Due to Gravity and Its Variation with Altitude and Depth
- Gravitational Potential Energy
- Escape Speed
- Earth Satellites
- Energy of an Orbiting Satellite
- Geostationary and Polar Satellites
- Escape Velocity
- Orbital Velocity of a Satellite
Properties of Bulk Matter
Mechanical Properties of Fluids
- Thrust and Pressure
- Pascal’s Law
- Variation of Pressure with Depth
- Atmospheric Pressure and Gauge Pressure
- Hydraulic Machines
- Streamline and Turbulent Flow
- Applications of Bernoulli’s Equation
- Viscous Force or Viscosity
- Reynold's Number
- Surface Tension
- Effect of Gravity on Fluid Pressure
- Terminal Velocity
- Critical Velocity
- Excess of Pressure Across a Curved Surface
- Introduction of Mechanical Properties of Fluids
- Archimedes' Principle
- Stoke's Law
- Equation of Continuity
- Torricelli's Law
Thermal Properties of Matter
- Heat and Temperature
- Measurement of Temperature
- Ideal-gas Equation and Absolute Temperature
- Thermal Expansion
- Specific Heat Capacity
- Change of State - Latent Heat Capacity
- Newton’s Law of Cooling
- Qualitative Ideas of Black Body Radiation
- Wien's Displacement Law
- Stefan's Law
- Anomalous Expansion of Water
- Liquids and Gases
- Thermal Expansion of Solids
- Green House Effect
Mechanical Properties of Solids
- Thermal Equilibrium
- Zeroth Law of Thermodynamics
- Heat, Internal Energy and Work
- First Law of Thermodynamics
- Specific Heat Capacity
- Thermodynamic State Variables and Equation of State
- Thermodynamic Process
- Heat Engine
- Refrigerators and Heat Pumps
- Second Law of Thermodynamics
- Reversible and Irreversible Processes
- Carnot Engine
- Isothermal Processes
- Adiabatic Processes
Behaviour of Perfect Gases and Kinetic Theory of Gases
- Molecular Nature of Matter
- Gases and Its Characteristics
- Equation of State of a Perfect Gas
- Work Done in Compressing a Gas
- Introduction of Kinetic Theory of an Ideal Gas
- Interpretation of Temperature in Kinetic Theory
- Law of Equipartition of Energy
- Specific Heat Capacities - Gases
- Mean Free Path
- Kinetic Theory of Gases - Concept of Pressure
- Assumptions of Kinetic Theory of Gases
- RMS Speed of Gas Molecules
- Degrees of Freedom
- Avogadro's Number
Oscillations and Waves
- Periodic and Oscillatory Motion
- Simple Harmonic Motion (S.H.M.)
- Simple Harmonic Motion and Uniform Circular Motion
- Velocity and Acceleration in Simple Harmonic Motion
- Force Law for Simple Harmonic Motion
- Energy in Simple Harmonic Motion
- Some Systems Executing Simple Harmonic Motion
- Damped Simple Harmonic Motion
- Forced Oscillations and Resonance
- Displacement as a Function of Time
- Periodic Functions
- Oscillations - Frequency
The pressure exerted by the weight of the atmosphere.
The atmosphere is a mixture of different gases. All these gas molecules together constitute some weight. By virtue of this weight, there is some pressure exerted by the atmosphere on all the objects.
This pressure is known as atmospheric pressure.
Value of atmospheric pressure at sea level is 1.01 x105
1atm = 1.01 x 105Pa
A long glass tube closed at one end and filled with mercury is inverted into a trough of mercury as shown in Fig. This device is known as the ‘mercury barometer’.
The space above the mercury column in the tube contains only mercury vapor whose pressure 'P' is so small that it may be neglected. Thus, the pressure at Point A=0.
The pressure inside the column at Point 'B' must be the same as the pressure at Point 'C', which is atmospheric pressure, 'Pa'.
Pa = ρgh
where ρ is the density of mercury and h is the height of the mercury column in the tube.
A pressure equivalent of 1 mm is called a torr (after Torricelli).
1 torr = 133 Pa.
The mm of Hg and torr are used in medicine and physiology.
In meteorology, a common unit is 'bar' and 'millibar'.
1 bar = 105 Pa
Pressure difference between the system and the atmosphere.
From relation P = Pa + ρgh where P= pressure at any point, Pa = atmospheric pressure.
We can say that Pressure at any point is always greater than the atmospheric pressure by the amount ρgh.
P - Pa = ρgh where
P= pressure of the system, Pa= atmospheric pressure,
(P - Pa) = pressure difference between the system and atmosphere.
hρg = Gauge pressure.
An open tube manometer is a useful instrument for measuring pressure differences. It consists of a U-tube containing a suitable liquid i.e., a low-density liquid (such as oil) for measuring small pressure differences and a high-density liquid (such as mercury) for large pressure differences.
One end of the tube is open to the atmosphere and the other end is connected to the system whose pressure we want to measure.
The pressure 'P' at 'A' is equal to the pressure at point 'B'. What we normally measure is the gauge pressure, which is (P − Pa), given by equation Pa = ρgh and is proportional to manometer height h.
The pressure is the same at the same level on both sides of the U-tube containing a fluid. For liquids, the density varies very little over wide ranges in pressure and temperature and we can treat it safely as a constant for our present purposes. Gases, on the other hand, exhibit large variations of densities with changes in pressure and temperature. Unlike gases, liquids are, therefore, largely treated as incompressible.
Absolute pressure is defined as the pressure above the zero value of pressure.
It is the actual pressure that a substance has.
It is measured against the vacuum.
Absolute pressure is measured relative to absolute zero pressure.
It is the sum of atmospheric pressure and gauge pressure.
P = Pa + hρg where P = pressure at any point, Pa = atmospheric pressure and hρg= gauge pressure.
Therefore P = Pa + Gauge Pressure. Where P = absolute pressure.
It is measured with the help of a barometer.
Problem: The density of the atmosphere at sea level is 1.29 kg/m3. Assume that it does not change with altitude. Then how high would the atmosphere extend?
From equation:- `"P" = "P"_a +rho"gh"`
`rho"gh"` = 1.29kg/m3 x 9.8m/s2 x hm = 1.01 x 105 Pa
`therefore` h = 7989m`~~`8 km
In reality, the density of air decreases with height. So does the value of g. The atmospheric cover extends with a decreasing pressure of over100 km. We should also note that the sea-level atmospheric pressure is not always 760 mm of Hg. A drop in the Hg level by 10 mm or more is a sign of an approaching storm.
Problem:- At a depth of 1000 m in an ocean (a) what is the absolute pressure? (b) What is the gauge pressure? (c) Find the force acting on the window of 20 cm × 20 cm of a submarine at this depth, the interior of which is maintained at sea-level atmospheric pressure. (The density of seawater is 1.03 × 103 kgm-3,g = 10ms–2.)
Here h = 1000m and `rho` = 1.03 x 103 kgm-3
(a) From Eq. P2 - P1 = `rho`gh, absolute pressure
`"P" = "P"_a + rho"gh"`
=`1.01 xx 10^5"Pa" + 1.03 xx 10^3"kgm"^-3xx10"ms"^-2xx1000"m"`
`=104.01 xx 10^5"Pa"`
(b) Gauge pressure is `"P" - "P"_a=rho"gh"="P"_g`
`"P"_g = 1.03 xx 10^3"kg m"^-3xx10"ms"^2xx1000"m"`
(c) The pressure outside the submarine is P = Pa + ρgh and the pressure inside it is Pa. Hence, the net pressure acting on the window is gauge pressure, Pg = ρgh. Since the area of the window is A = 0.04 m2, the force acting on it is
F = PgA = (103 × 105 Pa) × 0.04 m2 = 4.12 × 105 N
Shaalaa.com | Barometer and Manometer and U - Tube problems
A barometer tube reads 76 cm of mercury. If the tube is gradually inclined keeping the open end immersed in the mercury reservoir, will the length of mercury column be 76 cm, more than 76 cm or less than 76 cm?
Figure shows a capillary tube of radius r dipped into water. If the atmospheric pressure is P0, the pressure at point A is
The surface of water in a water tank on the top of a house is 4 m above the tap level. Find the pressure of water at the tap when the tap is closed. Is it necessary to specify that the tap is closed?
The heights of mercury surfaces in the two arms of the manometer shown in figure are 2 cm and 8 cm.
Atmospheric pressure = 1.01 × 105 N−2. Find (a) the pressure of the gas in the cylinder and (b) the pressure of mercury at the bottom of the U tube.
Consider the barometer shown in the following figure. If a small hole is made at a point P in the barometer tube, will the mercury come out from this hole?
The three vessels shown in the following figure have same base area. Equal volumes of a liquid are poured in the three vessels. The force on the base will be
The area of cross section of the wider tube shown in figure is 900 cm2. If the boy standing on the piston weighs 45 kg, find the difference in the levels of water in the two tubes.
The weight of an empty balloon on a spring balance is W1. The weight becomes W2when the balloon is filled with air. Let the weight of the air itself be w. Neglect the thickness of the balloon when it is filled with air. Also neglect the difference in the densities of air inside and outside the balloon.
(a) W2 = W1
(b) W2 = W1 + w
(c) W2 < W1 + w
(d) W2 > W1