Question

If $E,m,J$ and $G$ represent energy, mass, angular momentum and gravitational constant respectively, then the dimensional formula of $E{J}^2/m^5{G}^2$ is

• A. angle
• B. length
• C. mass
• D. time

Answer 1

Answer: (A)

$[E]=M{L}^2{T}^{-2}$
$[J]=[$ Moment of Inertia $]\times [$ Angular velocity $]$
$=M{L}^2{T}^{-1}$
$[G]=\left[\frac{F\cdot r^2}{M\cdot m}\right]=\frac{ML{T}^{-2}\cdot L^2}{M^2}=M^{-1}{L}^3{T}^{-2}$
Hence, $\left[\frac{E{J}^2}{m^5{G}^2}\right]=\frac{\left[M{L}^2{T}^{-2}\right]\cdot {\left[M{L}^2{T}^{-1}\right]}^2}{\left[M^5\right]\cdot {\left[M^{-1}{L}^3{T}^{-2}\right]}^2}$
$=M^0{L}^0{T}^0=[$ angle $]$