Question

If $E$ and $G$ respectively denote energy and gravitational constant, then $\frac{ E }{ G }$ has the dimensions of:

• A. $\left[ M ^{2}\right]\left[ L ^{-1}\right]\left[ T ^{0}\right]$
• B. $[ M ]\left[ L ^{-1}\right]\left[ T ^{-1}\right]$
• C. $[ M ]\left[ L ^{0}\right]\left[ T ^{0}\right]$
• D. $\left[ M ^{2}\right]\left[ L ^{-2}\right]\left[ T ^{-1}\right]$

Answer 1

Answer: (A)

Dimensional formula of energy
$ [E]=\left[M^{1} L^{2} T^{-2}\right] \ldots(I) $
Dimensional formula of gravitational constant
$ [G]=\left[M^{-1} L^{3} T^{-2}\right] \ldots \text { (II) } $
Dividing (I) by (II), we get:
Hence, $E / G==\left[M^{2} L^{-1} T^{0}\right]$