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Theory of Relativity

The basic concepts of relativity are explained in a very simplified way that are easy to understood by Mr. Vivek Sawhney in this YouTube Video… The video focuses upon the general discussion on Theory of Relativity….What is the theory of Relativity? What is time dilation and length contraction?

Theory of Relativity explained

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What is the theory of Relativity and where it’s concepts can be applied?

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A numerical problem from motion in 1 Dimension

A boy plays with a ball on a field surrounded by a fence which has a height of 2.5m . He kicks the ball vertically up from a height of 0.4m with a speed of 14 ms−1. (a) What is the maximum height of the ball above the fence? (b) What is the time taken to reach the maximum height? (c) How long is the ball above the height of the fence? (d) What is the velocity of the falling ball at the height of the fence? (e) What the acceleration of the ball after 1s ?

Asked John

Answer:

(a)

u=14 m/s

v=0 m/s at max height

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National Education Policy 2020 : Introduction

National Education Policy 2020 : Introduction, Read Along or Listen

If you are not getting time to read National Education Policy 2020, read along with this or listen to the reading. This is a verbatim reading out aloud of the National Education Policy 2020. The reader reads it in an impressive manner giving stress and tone variations at places to make the listening more enjoyable.

The fundamental principles

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Types of Errors and Errors in Combinations of Physical Quantities

Combination of Errors in a series of Measurements

 

Suppose the values obtained in several measurement are a1, a2, a3, …, an.

Arithmetic mean, amean = (a1+ a2 + a3+ … + an)/n

o Absolute Error: The magnitude of the difference between the true value of the quantity and the individual measurement value is called absolute error of the measurement. It is denoted by a| (or Mod of Delta a). The mod value is always positive even if Δa is negative. The individual errors are:

Δa1 = amean – a1, Δa2 = amean – a2, ……. ,Δan = amean – an

o Mean absolute error is the arithmetic mean of all absolute errors. It is represented by Δamean.

Δamean = (|Δa1| + |Δa2| +|Δa3| + …. +|Δan|) / n

For single measurement, the value of ‘a’ is always in the range amean± Δamean

So, a = amean ± Δamean Or amean – Δamean< a <amean + Δamean

o Relative Error: It is the ratio of mean absolute error to the mean value of the quantity measured.

Relative Error = Δamean / amean

o Percentage Error: It is the relative error expressed in percentage. It is denoted by δa.

δa = (Δamean / amean) x 100%

Combination of Errors

If a quantity depends on two or more other quantities, the combination of errors in the two quantities helps to determine and predict the errors in the resultant quantity. There are several procedures for this.

Suppose two quantities A and B have values as A ± ΔA and B ± ΔB. Z is the result and ΔZ is the error due to combination of A and B.

Criteria Sum or Difference Product Raised to Power
Resultant value Z Z = A ± B Z = AB Z = Ak
Result with error Z ± ΔZ = (A ± ΔA) + (B ± ΔB) Z ± ΔZ = (A ± ΔA) (B ± ΔB) Z ± ΔZ = (A ± ΔA)k
Resultant error range ± ΔZ = ± ΔA ± ΔB ΔZ/Z = ΔA/A ± ΔB/B
Maximum error ΔZ = ΔA + ΔB ΔZ/Z = ΔA/A + ΔB/B ΔZ/Z = k(ΔA/A)
Error Sum of absolute errors Sum of relative errors k times relative error

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Vivek Sir demonstrating Experiment on measuring resistance

Types of Errors

Types of errors
Types of Errors

Error is deviation from the true value as a result of measurement. Due to various reason affecting the measurements there are different types of errors that creep in whenever we make a measurement. 

Types of Errors

 

Systematic Errors

Errors which can either be positive or negative are called Systematic errors. For a particular measurement device, it will be either positive or negative. The causes of such errors are known and hence they can be avoided or accounted for. They are of following types:

1. Instrumental errors:

These arise from imperfect design or calibration error in the instrument. Worn off scale, zero error in a weighing scale are some examples of instrument errors.

2. Imperfections in experimental techniques:

If the technique is not accurate (for example measuring temperature of human body by placing thermometer under armpit resulting in lower temperature than actual) and due to the external conditions like temperature, wind, humidity, these kinds of errors occur.

3. Personal errors:

Errors occurring due to human carelessness, lack of proper setting, taking down incorrect reading are called personal errors.

These errors can be removed by:

o Taking proper instrument and calibrating it properly.

o Experimenting under proper atmospheric conditions and techniques.

Removing human bias as far as possible

Random Errors

Errors which occur at random with respect to sign and size are called Random errors. The errors whose actual cause is not known and cannot be accounted for. However, the random errors come on either side, i.e. the repeated measurements result in positive as well as negative errors. Therefore the random error in a measurement can be minimized by repeating the experiment a number of times and taking the mean. Since some of the measurements will have positive errors and the rest negative, taking the mean of all results of measurements will take us closer to the true value. Greater the number of repetitions, greater will be the closeness to the accurate value.

o These occur due to unpredictable fluctuations in experimental conditions like temperature, voltage supply, mechanical vibrations, personal errors etc.

o Smallest value that can be measured by the measuring instrument is called its least count. Least count error is the error associated with the resolution or the least count of the instrument.

o Least count errors can be minimized by using instruments of higher precision/resolution and improving experimental techniques (taking several readings of a measurement and then taking a mean).

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Schrodinger’s Cat in Daily Life

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