Physics

If universal gravitational constant (G), speed of light (c), and time (t) are base units then the dimensional formula of mass can be represented as?


ANSWER

$$[G^{-1}c^3t^1]$$


SOLUTION
$$G=N{ m }^{ 2 }{ kg }^{ -2 }\\ \quad \quad =(kg\quad m{ s }^{ -2 }){ m }^{ 2 }{ kg }^{ -2 }\\ \quad \quad \quad ={ kg }^{ -1 }{ m }^{ 3 }{ s }^{ -2 }$$
Speed of light $$C=\quad m{ s }^{ -1 }$$
$${ (m{ s }^{ -1 }) }^{ 3 }={ m }^{ 3 }{ s }^{ -3 }$$= $${ C }^{ 3 }$$
t= s
$${ G }^{ -1 }\times { C }^{ 3 }\times t={ ({ kg }^{ -1 }{ m }^{ 3 }{ s }^{ -2 }) }^{ -1 }\times ({ m }^{ 3 }{ s }^{ -3 })\times s\\ \quad \quad \quad \quad =\quad kg$$
= mass
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