Question

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?

• A. $\left[G^1{c}^3{t}^1\right]$
• B. $\left[G^{-1}{c}^3{t}^1\right]$
• C. $\left[G^{-1}{c}^{-2}{t}^{-1}\right]$
• D. $\left[G^1{c}^{-3}{t}^{-1}\right]$

Answer 1

Answer: (B)

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

$G=N{m}^2{kg}^{-2}=\left(kgm{s}^{-2}\right)m^2{kg}^{-2}={kg}^{-1}{m}^3{s}^{-2}$

Speed of light $C=m{s}^{-1}$

${\left(m{s}^{-1}\right)}^3=m^3{s}^{-3}$= $C^3$

t= s

$G^{-1}\times C^3\times t={\left({kg}^{-1}{m}^3{s}^{-2}\right)}^{-1}\times \left(m^3{s}^{-3}\right)\times s=kg$

= mass