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प्रश्न
If two quantities have same dimensions, do they represent same physical content?
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उत्तर
No, even if two quantities have the same dimensions, they may represent different physical contents.
Example: Torque and energy have the same dimension but represent different physical contents.
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संबंधित 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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Choose the correct statements(s):
Find the dimensions of pressure.
Find the dimensions of
(a) angular speed ω,
(b) angular acceleration α,
(c) torque τ and
(d) moment of interia I.
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The symbols have standard meanings.
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\[v = \sqrt{\frac{P}{\rho}},\]
where v = velocity, ρ = density, P = pressure
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(d) equal to zero.
A vector \[\vec{A}\] makes an angle of 20° and \[\vec{B}\] makes an angle of 110° with the X-axis. The magnitudes of these vectors are 3 m and 4 m respectively. Find the resultant.
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\[\begin{array}x & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\ y & 2 & 8 & 18 & 32 & 50 & 72 & 98 & 128 & 162 & 200\end{array}\]
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 changes in a function y and the independent variable x are related as
\[\frac{dy}{dx} = x^2\] . Find y as a function of x.
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