Description of Errors in Measurement

Errors in Measurement

The following errors are likely to occur in the measurement of a physical quantity:

(1) Systematic Errors (arise due to known causes. The experimenter has control over the errors)
(2) Random Errors (arise due to unknown causes. The experimenter has no control over the errors)

(1) Systematic Errors:

When a measurement always has the same error (i.e. the nature or sign of the error is always of the same type, positive or negative), it is called systematic error.

Systematic errors occur due to known causes. These errors can be removed by knowing the causes.

Types of Systematic Errors:

(i) Constant Errors: If the measuring instrument is faulty from the point of view of its structure or design. That is, if the measurement marks made on the measuring instrument are wrong (faulty graduations), then by using such an instrument the error is always the same in all the observations. Such an error is called a constant error.

To remove static errors, an error-free measuring instrument should be used in place of the faulty measuring instrument and if this is not possible, then the nature of the error in the faulty instrument should be determined and measurements should be made as many times as possible.

(ii) Errors Due to Instruments: Such measuring instruments are error-free from the point of view of structure or design, but their excessive use causes defects in these instruments. Like zero error in vernier calipers or screw gauges, etc. Before starting the observation, such errors are found in all the measuring instruments used so that the final result of the measurement can be accurate.

(iii) Personal Errors: Those errors which arise due to the carelessness of the experimenter or the person doing the measurement are called personal errors. It does not depend on measuring instruments. This error can be reduced by increasing caution and taking readings correctly.

(iv) Errors caused by external factors (Errors due to External Reasons): Errors caused in observation due to changes in pressure, temperature, humidity, air velocity, etc. while taking observations are called errors caused by external factors.

These types of errors can be eliminated by adopting appropriate precautions and making possible arrangements to control environmental change. Can be done.

(2) Random Errors:

Such errors over which the experimenter has no control are called irregular errors. If the temperature, pressure, or humidity of the environment suddenly changes rapidly during observation or the supply voltage changes suddenly in any electrical experiment or the value of the earthquake exceeds the normal limit, then such changes have different effects in different experiments which affects the value of observation. These errors can be eliminated to a great extent by taking measurements several times and finding their average. Actual value can be found.

Read more

Description of Force and their Types

Force:

Force is a push or pull by which the state of the object changes or tends to change.

Types of forces:

There are two types of forces-

1.) Contact Force
2.) Non-Contact Force

1.) Contact force:

When there is physical contact between the two objects by push or pull then it is known as contact force.

For Example:

i.) When a coiled spring is stretched (pulled), the two ends of the spring must be in actual contact with the person's hands.
ii.) Kicking a football, and pulling a cart are also contact forces.

Types of Contact Force:

I.) Applied Force
II.) Frictional Force
III.) Normal Force
IV.) Tension Force
V.) Air Resistance (Drag Force)
VI.) Elastic or Restoring force

I.) Applied Force:

When a force is exerted by a person or an object to another person or object then this force is known as applied force.

$F=ma$

Example: Pushing a shopping cart, pulling a door open.

II.) Frictional Force:

When two surfaces are in motion relative to each other and in contact then a force acting in the opposite direction of the motion of one surface over the other is called the force of friction. The frictional force is also called the force of friction or simply friction.

$F=\mu R$

A smooth surface exerts a lesser force of friction than a rough surface. The rolling frictional froce is always less than the sliding frictional force.

Types of Friction Force:

i.) Static Friction:

When the frictional force is applied on the object due state of the rest of the object then frictional force is known as static friction.

ii.) Kinetic Friction:

When the frictional force is applied to the object due motion of the object then frictional force is known as dynamic friction.

iii.) Limiting Friction:

The maximum value of static frictional force is known as limiting friction.

Example: Rubbing hands together, a car’s brakes stopping a vehicle

III.) Normal Reaction Force:

When an object is placed on a surface (or another object), the object exerts a force on the surface (or another object) vertically downwards. However, the object does not move in the direction of the force. This is because the surface (or another object) exerts an equal and opposite force on the object vertically upwards. then this force is called normal reaction force.

$Normal \: reaction \: force (N) = Weight \: of \: the \: object (mg) $

Example: A book resting on a table, a person standing on the ground.

IV.) Tension force:

The force on the string, rope, or cable due to pulled tight is known as Tension. Force is transmitted through a s when pulled tight.

Example: A person pulling a rope in a tug-of-war, a hanging lightbulb.

V.) Air Resistance (Drag Force):

It is a type of friction force that acts against objects moving through the air.

Example: A parachute slowing down a skydiver, wind resistance on a car.

VI.) Spring Force (Elastic Force Or Restoring force):

A force that always acts in the opposite direction of the object's displacement is known as elastic or restoring force.

Example: A compressed spring in a toy, a rubber band being stretched.

2. Non-Contact Forces (Act at a distance)

I.) Gravitational Force (F)

The force of attraction between two heavy objects is directly proportional to the product of their masses and inversely proportional to the square of the distance between them.

$F=G \frac{m_{1}m_{2}}{r^{2}}$

This force is most effective between very heavy objects like satellites, Planets Su,n and Stars.

Example: Objects falling to the ground, Earth’s gravity keeping the Moon in orbit.

II.) Electromagnetic Force:

When electric force and magnetic force are applied perpendicular to each other on charged particles then a force acts perpendicular to both this force is known as electromagnetic force.

The force between charged objects include both electric force and magnetic forces.

Example: Lightning (electric force), magnets attracting iron nails.

i.) Magnetic Force:

The force between magnetic materials, either attracting or repelling is known as magnetic force. The magnitude of magnetic force due to moving charge is described by Lorentz's law ($F=qvB sin \theta$)and direction is described by Fleming's left-hand rule. Similarly, the magnetic force due to the conductor is described by the formula $F=iBl sin\theta$ that is deduced by Lorentz's law, and the direction of force in a conductor is also described by Fleming's left-hand rule.

Example: A compass needle pointing north, fridge magnets sticking to a fridge.

ii.) Electric Force:

The attraction and repulsion force between the charges is known as the electric force. The magnitude of this force is described by Coulomb's law and the direction is described by the vector form of Coulomb's Law.

$F=\frac{1}{4\pi \epsilon_{\circ} K} \frac{q_{1}q_{2}}{r^{2}}$

IV.) Nuclear Forces: The force between the nucleons (i.e. proton and neutron) is known as nuclear force. Nuclear forces are two types.

i.) Strong Nuclear Force:

It is the very strongest and short-distance force that holds protons and neutrons together in an atomic nucleus.

ii.) Weak Nuclear Force:

When the nucleus is involved in radioactive $\beta$ decay then the force between the particles is known as weak nuclear force. The force is involved in the reaction of nuclear fission and fusion.

Example: The energy released in nuclear reactions, like in the Sun or nuclear power plants.

Read more

Finding Significant Figures in a Measurement

What is significant Figure?

The total number of digits (i.e. doubtful digit and confirm digits) in any measurement is known as significant figure.

Or

The digits that reflect the precision of the measurement are called significant figures.

Counting of Significant Figures in any Measurement:

Knowing the significant figures in a measure is based on the following rules-

(1) All non-zero numbers are significant figures.

For example, $46.3598$ has $6$ significant figures.

(2) All zero numbers between two non-zero numbers are significant figures.

For example, $600.8049$ has $7$ significant figures.

(3) If there is no non-zero number before the decimal point, then all the digits in the number except the zero numbers immediately after the decimal point are significant figures.

For example, $0.002809$ has $4$ significant figures.

(4) The zero after any non-zero digit to the right of the decimal point is a significant figure.

For example, $0.46920$ has $0$ significant figures.

(5) If a number is multiplied by a power of $10$, it does not affect the number of significant figures.

For example, $6.75\times 10^{3}$ has $3$ significant figures.

(6) Choosing different units does not change the number of significant figures.

For example, if a measurement is $2346 km$, then in different units, this measurement will be $23460 m$, $2346000 cm$ or $23460000 mm$. Here, the number of significant figures in each measurement is $4$.

Read more

Limitations of Dimensional Analysis

Limitations of Dimensional Analysis:

(1) It is not possible to find the numerical value of constants $k$ (dimensionless) present in the formulas by this method. It can be obtained by experiment or other method.

(2) If any physical quantity depends on more than three quantities, then the mutual relation between these quantities cannot be established by this method. However, the dimensional correctness of any given equation of this type can be checked.

(3) If any physical quantity depends on only three physical quantities, but the dimensions of two of the three quantities are the same, then also the mutual relation between these quantities cannot be established by the dimensional method, but the dimensional correctness can be checked.

(4) If an equation has more than one term on one side, like $v=u+at$ (Here two terms on the right side), then this equation cannot be derived by dimensional method. That is, such relations cannot be derived in which there is a positive $(+)$ or negative $(-)$ sign anywhere. But whether the equation is dimensionally correct or not, can be checked.

(5) Deduction of equations containing trigonometric ratios ($ sin \theta$, $cos \theta$, $tan \theta$, etc.), variable exponential ($e^{x}$) and logarithmic ($log\:x$) terms is not possible by dimensional analysis method, but their dimensional truth can be checked.

(6) Whether a physical quantity is vector or scalar cannot be determined by the dimensional analysis method.

(7) If the constant in an equation is not dimensionless, then the dimensional analysis method cannot be used for the deduction of that equation.

(8) For a physical relation represented by an equation to be true, it is a necessary condition for this equation to be in dimensional balance, but only dimensional balance is not sufficient for the physical relation to be true. That is,

"Even if the equation is true physically and mathematically, it may not be true dimensionally."

Read more

Difference between Forced Vibrations and Resonant Vibrations

Forced Vibrations:

1. The vibrations of a body under an external periodic force of frequency different from the natural frequency of the body, are called forced vibrations.

2. The amplitude of vibration is small.

3. The vibrations of the body are not in phase with the external periodic force.

4. These vibrations last for a very short time after the periodic force has ceased to act.

Resonant Vibrations:

1. The vibrations of a body under an external periodic force of frequency exactly equal to the natural frequency of the body, are called resonant vibrations.

2. The amplitude of vibration is very large.

3. The vibrations of the body are in phase with the external periodic force.

4. These vibrations last for a long time after the periodic force has ceased to act.

Read more

Difference between Natural Vibrations and Damped Vibrations

Natural Vibrations:

1. The amplitude of natural vibrations or free vibrations remains constant and the vibrations continue forever.

2. Natural vibrations never lose energy during vibrations.

3. There are no external forces acting on the vibrating body. The vibrations are only under the restoring force.

4. The frequency of vibrations depends on the size and shape of the body and it remains constant.

Damped Vibrations:

1. The amplitude of damped vibrations gradually decreases or reduces with time and ultimately the vibrations cease.

2. In each vibration, there is some energy loss in the form of heat.

3. Besides the restoring force, a frictional or damping force acts on the body to oppose its motion.

4. The frequency of damped vibrations is less than the natural frequency. The decrease in frequency of vibrations depends on the damping force.

Read more

Difference between Natural (Free) Vibrations and Forced Vibrations

Natural (Free) Vibrations:

1.) The vibrations of a body in absence of any resistive or external force are called natural vibrations.

2.) The frequency of vibration depends on the shape and size of the body.

3.) The frequency of vibration remains Constant.

4.) The amplitude of vibration remains constant with time (in absence of surrounding medium).

Forced Vibrations:

1.) The vibrations of a body in a medium in presence of an external periodic force are called forced vibrations.

2.) The frequency of vibration is equal to the frequency of the applied force.

3.) The frequency of vibration changes with change in the frequency of the applied force.

4.) The amplitude of vibration depends on the frequency of the applied force.

Read more

Renewable Energy Sources

Renewable Energy Sources:

Various renewable energy sources are as follows:

Solar Energy:

The solar energy is a non conventional energy source. It is very cost effective clean and non polluted renewable energy source and reduces the greenhouse gas effect.

The Solar Energy is derived from the Sun radiation and can be utilised by photosynthesis, photo voltaic cell, photo thermoelectric system.

The sun release the enormous amount of energy and it's rate of radiation is $3.7 \times 10^{20}$ megawatt while the earth receive the radiation at rate by $1.85 \times 10^{11}$ megawatt. So energy radiation by the sun is several times more than the consumption of radiation in the earth.

Advantages:

1.) It is very clean energy.

2.) It is non polluted energy source.

3.) It is zero cost energy source and low maintenance cost.

4.) It has zero noise in operation.

Disadvantages :

1.) Energy source cannot utilise properly at night, cloudy atmosphere and rainy day.

2.) It has required large surface area to collect the energy source from Sun.

Hydro energy:

The hydro energy is derived from moving and falling water which convert into mechanical energy and utilise for production of electrical energy through turbine.

The water is stored in reservoir or dam has high potential energy and when water flow or fall under the gravity then it rotate the turbine and produces the electricity.

Advantages:

1.) It is very clean energy source.

2.) It produce zero pollution.

3.) It has zero fuel cost.

4.) It requires low maintenance cost.

5.) It is reliable energy source.

Disadvantages:

1.) It can cause climate change due to high amount of storage of water in mountains.

2.) It can cause flood and disrupt ecosystem.

Wind energy:

Wind energy is also non polluting energy source and it has tremendous potential to fulfill the demand of energy of the country.

It is estimated that only $2 \%$ of solar energy fall on the earth and converted into kinetic energy of the atmospheric molecules or atoms. The highest kinetic energy of atmosphere is found in the lower to mid troposphere layer which is lowest layer of atmosphere because of that this kinetic energy can be easily converted to the mechanical energy which can futher utilise for the production of electrical energy and other energy production.

Advantage:

1.) It is useful for remote places for the production of electricity.

2.) The availability of the source is zero cost.

Disadvantages:

1.) This energy source cannot be properly utilised where wind is available at very higher location.

2.) It is unreliable because flow of wind cannot be continuous all the time.

Wave Energy:

The wave energy is available on the surface of sea. The floating propeller is placed on the surface of the shallow water near to shores and due to motion of wave propeller get start to rotate and this rotational energy is used to derive the turbines.

Advantages:

1.) This is clean or cheap energy source.

2.) The size of the machine for the collection of wave is comparatively smaller than solar device.

Disadvantages:

Corrrosion of material used in plant.

Geothermal energy:

This is the energy is produced due to hot rocks present inside the earth. The temperature of the earth increases with increase in depth below the surface of the earth. The hot molted rock is present at center or core of the earth this causes volcano action. The hot rock is pull out from volcano and used to produce the steam by heating water. This steam is further utilised for the operation of turbine to produce the electricity.

Advantages:

It is cheap source which requires small area for the operation or production of the electricity.

Disadvantages:

1.) It causes the air pollution due to production of gases like $H_{2}S$ and $NH_{3}$in steam waste.

2.) It is also causes noise pollution due to drilling operation.

Read more

Basics of Third Generation Solar Cells and Their Types

Third Generation Solar Cells :

They are proposed to be very different from the previous semiconductor devices as they do not rely on a traditional p-n junction to separate photogenerated charge carriers.

For space applications quantum well devices (quantum dots, quantum ropes etc.) and devices incorporating carbon nanotubes are being studied with a potential for up to $45 %$ production efficiency.

For terrestrial applications, these new devices include photoelectrochemical cells, polymer solar cells, nanocrystal solar cells,dye sensitized solar cells and are still in the research phase.

Types of Third Generation Solar Cells :

A.) Organic Photovoltaic Cell :

1. The solar cells based on organic semiconductor can provide a low cost alternative for photovoltaic solar.

2. The thickness of the active layer of organic solar cells is only $100 nm$ thin, which is about $1000$ times thinner than the crystalline silicon solar cells, and it is about 10 times thinner than the current inorganic thin film solar cells.

3. In the low material consumption per solar cell and the relatively simpler cell processing of organic semiconductors, there is a large potential for low cost large area solar cells.

4. Due to this reason, there is a considerable interest in organic photovoltaic devices.

5. Their principal advantage is that they are flexible and can bend without breaking, unlike $Si$, which is brittle.

6. They are also very light and cheap.

7. They may folded or cut into required size and can still be used.

B.) Dye Sensitized Solar Cell (DSSC):

1. Dye Sensitized Solar Cell converts any visible light into electrical energy.

2. The dye sensitized solar cells can be considered as a thin film solar cell device. This technology is not yet commercialized but is on the verge of commercialization.

3. The dye sensitized solar cells can be made flexible. It has a very good potential for being a low cost effect solar cell technology.

4. This is mainly possible because of the large availability and low cost of the ingredient material as well as due to the low processing temperatures.

5. The dye sensitized solar cells is a photo-electro-chemical device. In its operation it involves a photon, an electron and a chemical reaction.

6. The operation of dye sensitized solar cell is considered similar to that of a photosynthesis process.

7. The DSSC has a number of attractive features; it is simple to make using conventional roll-printing techniques, is semi-flexible and semi- transparent which offers different type of uses not applicable to glass-based systems, and cost of most of the materials used in DSSC are very low.

Read more

Fluid and it's important characteristics

What are fluids?

A fluid is a substance that can flow. The fluid has no definite shape. Its shapes depends upon the containing vessel i.e. It cannot resist shearing stress and adjust their form accordingly.

What is ideal fluid?

Those fluid which have zero compressibility and zero viscosity is called ideal fluid.

Important characteristics of fluids :

(1) Random Molecular Arrangment: The atoms or molecules within a fluid are arranged randomly unlike the structured arrangment in a solid.

(2) Inability to resist shearing stress: A fluid cannot withstand tangential or shearing stress for an indefinite period. When a shearing stress is applied, it begins to flow.

(3) No fixed shape: A fluid has no definite shape of its own and it adopt the shape of their container. Consequently, a fluid does not possess modulus of rigidity.

(4) Ability to exert perpendicular force: A fluid exert a force in a direction normal to its surface. Consequently, a fluid does possess bulk modulus of rigidity.

Read more