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प्रश्न
“It is more important to have beauty in the equations of physics than to have them agree with experiments”. The great British physicist P. A. M. Dirac held this view. Criticize this statement. Look out for some equations and results in this book which strike you as beautiful.
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उत्तर १
An equation which agrees with experiment must also be simple and hence beautiful. We have some simple and beautiful equations in Physics such as
- E = mc2 (Energy of light)
- E = hv (Energy of a photon)
- KE = 1/2mv2(Kinetic energy of a moving particle)
- PE = mgh (Potential energy of a body at rest)
- W = F.d (Work done)
All have the same dimensions. One experiment shows dependency of energy on speed, the other shows dependency on frequency & displacement. That's the beauty of equations in Physics coming from different experiments.
उत्तर २
Generally it is considered that physics is a dry subject and its main aim is to give qualitative and quantitative treatment i.e., any derived relation or equation must be verified through experimentation. It is felt that truth of an equation is more important than the simplicity, wonderfulness, symmetry or beauty of the equation. But frankly, if a relation is true to experimentation and simultaneously it is simple, interesting, symmetrical, wonderful or beautiful, it will certainly add to the charm of the relation.
संबंधित प्रश्न
India has had a long and unbroken tradition of great scholarship — in mathematics, astronomy, linguistics, logic and ethics. Yet, in parallel with this, several superstitious and obscurantistic attitudes and practices flourished in our society and unfortunately continue even today — among many educated people too. How will you use your knowledge of science to develop strategies to counter these attitudes ?
What are the dimensions of the ratio of the volume of a cube of edge a to the volume of a sphere of radius a?
Suppose a quantity x can be dimensionally represented in terms of M, L and T, that is, `[ x ] = M^a L^b T^c`. The quantity mass
\[\int\frac{dx}{\sqrt{2ax - x^2}} = a^n \sin^{- 1} \left[ \frac{x}{a} - 1 \right]\]
The value of n is
Choose the correct statements(s):
(a) All quantities may be represented dimensionally in terms of the base quantities.
(b) A base quantity cannot be represented dimensionally in terms of the rest of the base quantities.
(c) The dimensions of a base quantity in other base quantities is always zero.
(d) The dimension of a derived quantity is never zero in any base quantity.
Find the dimensions of linear momentum .
Let x and a stand for distance. Is
\[\int\frac{dx}{\sqrt{a^2 - x^2}} = \frac{1}{a} \sin^{- 1} \frac{a}{x}\] dimensionally correct?
Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?
Can you have \[\vec{A} \times \vec{B} = \vec{A} \cdot \vec{B}\] with A ≠ 0 and B ≠ 0 ? What if one of the two vectors is zero?
Let \[\vec{C} = \vec{A} + \vec{B}\]
Let \[\vec{A} \text { and } \vec{B}\] be the two vectors of magnitude 10 unit each. If they are inclined to the X-axis at angle 30° and 60° respectively, find the resultant.
Let \[\vec{a} = 4 \vec{i} + 3 \vec{j} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j}\]. Find the magnitudes of (a) \[\vec{a}\] , (b) \[\vec{b}\] ,(c) \[\vec{a} + \vec{b} \text { and }\] (d) \[\vec{a} - \vec{b}\].
A spy report about a suspected car reads as follows. "The car moved 2.00 km towards east, made a perpendicular left turn, ran for 500 m, made a perpendicular right turn, ran for 4.00 km and stopped". Find the displacement of the car.
Let \[\vec{a} = 2 \vec{i} + 3 \vec{j} + 4 \vec{k} \text { and } \vec{b} = 3 \vec{i} + 4 \vec{j} + 5 \vec{k}\] Find the angle between them.
If \[\vec{A} , \vec{B} , \vec{C}\] are mutually perpendicular, show that \[\vec{C} \times \left( \vec{A} \times \vec{B} \right) = 0\] Is the converse true?
Give an example for which \[\vec{A} \cdot \vec{B} = \vec{C} \cdot \vec{B} \text{ but } \vec{A} \neq \vec{C}\].
Round the following numbers to 2 significant digits.
(a) 3472, (b) 84.16. (c)2.55 and (d) 28.5
In a submarine equipped with sonar, the time delay between the generation of a pulse and its echo after reflection from an enemy submarine is observed to be 80 s. If the speed of sound in water is 1460 ms-1. What is the distance of an enemy submarine?
Jupiter is at a distance of 824.7 million km from the Earth. Its angular diameter is measured to be 35.72˝. Calculate the diameter of Jupiter.
High speed moving particles are studied under
