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प्रश्न
Some of the most profound statements on the nature of science have come from Albert Einstein, one of the greatest scientists of all time. What do you think did Einstein mean when he said : “The most incomprehensible thing about the world is that it is comprehensible”?
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उत्तर १
The whole of physical world is complex in nature. The biological world has its own complexities. Moreover, vastly different orders of magnitudes are involved in space, time and mass. Inspite of all this, almost all the physical phenomena can be expressed in terms of few basic laws. When viewed in this context, Einstein’s statement becomes very clear
उत्तर २
The Physical world around us is full of different complex natural phenomena so the world is in-comprehensible. But with the help of study and observations it has been found that all these phenomena are based on some basic physical laws and so it is comprehensible.
संबंधित प्रश्न
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
Choose the correct statements(s):
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 Planck's constant h from the equation E = hv where E is the energy and v is the frequency.
Find the dimensions of the specific heat capacity c.
(a) the specific heat capacity c,
(b) the coefficient of linear expansion α and
(c) the gas constant R.
Some of the equations involving these quantities are \[Q = mc\left( T_2 - T_1 \right), l_t = l_0 \left[ 1 + \alpha\left( T_2 - T_1 \right) \right]\] and PV = nRT.
The height of mercury column in a barometer in a Calcutta laboratory was recorded to be 75 cm. Calculate this pressure in SI and CGS units using the following data : Specific gravity of mercury = \[13 \cdot 6\] , Density of \[\text{ water} = {10}^3 kg/ m^3 , g = 9 \cdot 8 m/ s^2\] at Calcutta. Pressure
= hpg in usual symbols.
Test if the following equation is dimensionally correct:
\[h = \frac{2S cos\theta}{\text{ prg }},\]
where h = height, S = surface tension, ρ = density, I = moment of interia.
Is it possible to add two vectors of unequal magnitudes and get zero? Is it possible to add three vectors of equal magnitudes and get zero?
Can you add two vectors representing physical quantities having different dimensions? Can you multiply two vectors representing physical quantities having different dimensions?
Is the vector sum of the unit vectors \[\vec{i}\] and \[\vec{i}\] a unit vector? If no, can you multiply this sum by a scalar number to get a unit vector?
The component of a vector is
The radius of a circle is stated as 2.12 cm. Its area should be written as
Let the angle between two nonzero vectors \[\vec{A}\] and \[\vec{B}\] be 120° and its resultant be \[\vec{C}\].
Two vectors have magnitudes 2 unit and 4 unit respectively. What should be the angle between them if the magnitude of the resultant is (a) 1 unit, (b) 5 unit and (c) 7 unit.
A carrom board (4 ft × 4 ft square) has the queen at the centre. The queen, hit by the striker moves to the from edge, rebounds and goes in the hole behind the striking line. Find the magnitude of displacement of the queen (a) from the centre to the front edge, (b) from the front edge to the hole and (c) from the centre to the hole.
Two vectors have magnitudes 2 m and 3m. The angle between them is 60°. Find (a) the scalar product of the two vectors, (b) the magnitude of their vector product.
A curve is represented by y = sin x. If x is changed from \[\frac{\pi}{3}\text{ to }\frac{\pi}{3} + \frac{\pi}{100}\] , find approximately the change in y.
The electric current in a charging R−C circuit is given by i = i0 e−t/RC where i0, R and C are constant parameters of the circuit and t is time. Find the rate of change of current at (a) t = 0, (b) t = RC, (c) t = 10 RC.
Write the number of significant digits in (a) 1001, (b) 100.1, (c) 100.10, (d) 0.001001.
