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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
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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 = mc^{2}, 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 ...

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 = mc^{2}, 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 ...

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}}}