Correct Answer - Option 2 : Specific Gravity
The correct answer is Specific Gravity.
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Dimensions: When a derived quantity is expressed in terms of fundamental quantities, it is written as a product of different powers of the fundamental quantities.
- The powers to which fundamental quantities must be raised in order to express the given physical quantity are called its dimensions.
- A quantity without dimension will usually be a ratio of two quantities with similar dimensions and hence, will cancel out. Thus, they will have no units and known as dimensionless quantity.
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Specific gravity: It is the ratio of the density of a substance to the density of a given reference material i.e.,
\(Specific\;gravity\;\left( \rho \right) = \frac{{Density\;of\;the\;object\;\left( {{\rho _{object}}} \right)}}{{Density\;of\;water\;\left( {{\rho _{water}}} \right)}}\)
\( \Rightarrow Specific\;gravity = \frac{{\left[ {M{L^3}{T^0}} \right]}}{{\left[ {M{L^3}{T^0}} \right]}} = 1\)
∴ Specific gravity is a dimensionless quantity