principle of homogeneity of dimensions - A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ mo of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes : [math] m = \frac{m_0}{[(1-v^2)]^{\frac{1}{2}}} [/math]. Guess where to put the missing c.

A famous relation in physics relates ‘moving mass’ m to the ‘rest mass’ mo of a particle in terms of its speed v and the speed of light, c. (This relation first arose as a consequence of special relativity due to Albert Einstein). A boy recalls the relation almost correctly but forgets where to put the constant c. He writes : [math] m = \frac{m_0}{[(1-v^2)]^{\frac{1}{2}}} [/math]. Guess where to put the missing c.

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Dimensional Analysis - Principle of Homogeneity, Applications and ...

We quantify the size and shape of things using dimensional measurement. ... Dimensional analysis is also called Factor Label Method or Unit Factor Method because we ... Using Dimensional Analysis to Check the Correctness of Physical Equation ... Principle of Homogeneity states that dimensions of each of the terms of a ...

For more information, see Dimensional Analysis - Principle of Homogeneity, Applications and ...

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In layman's terms, why is Einstein's famous equation 'E = mc^2' and ...

He was explaining some basic physics mostly in layman's terms which wss ... The speed of light is squared in the formula because the equation would be ... Since c has dimensions of l/t (meters/second in SI units), there is no choice; ... How can E =mc^2 be true if light doesn't have mass? ... or “It's just a fundamental truth.

For more information, see In layman's terms, why is Einstein's famous equation 'E = mc^2' and ...

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matter | Definition, Characteristics, States, Examples, & Facts ...

Feb 25, 2021 ... When a material changes state, its smallest units, called molecules, ... instantaneously to attempts to change its state of rest or motion. ... Einstein's theory of special relativity (1905) shows that matter (as ... E = mc², where E is energy, m is mass, and c is the speed of light. ... physical science: Greek physics.

For more information, see matter | Definition, Characteristics, States, Examples, & Facts ...

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matter | Definition, Characteristics, States, Examples, & Facts ...

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Teja (last edited 6 months ago) (Student, UG2 Grade)

Given relation: m = \frac{m_0}{(1 - v^2)^{\frac{1}{2}}}

Missing constant: Speed of light = c

Step 1: Writing the dimensional formulae for given physical quantities

Moving mass [math] m = [M^1 L^0 T^0] [/math]

Rest mass [math] m = [M^1 L^0 T^0] [/math]

Speed [math]v=[M^0L^1T^{-1}]\ \Rightarrow\ v^2=[M^0L^2T^{-2}][/math]

Speed of light [math] c = [M^0 L^1 T^{-1}] [/math]

Step 2: Setting up a correct relation

According to the principle of homogeneity, the given formula will be dimensionally correct only if the dimensions of L.H.S and R.H.S are the same. This is only possible when the factor (1 - v^2)^{\frac{1}{2}} has no dimension.

Just dividing v^2 \text{ by } c^2 makes this possible. Therefore, the correct relationship is m = \frac{m_0}{(1 - \frac{v^2}{c^2})^{\frac{1}{2}}}