If E and G respectively denote energy and gravitational constant, then ( E / G ) has the dimensions of:

Question

If E and G respectively denote energy and gravitational constant, then ( E / G ) has the dimensions of: (A) [ M 2][ L -1][ T 0] (B) [ M ][ L -1][ T -1] (C) [ M ][ L 0][ T 0] (D) [ M 2][ L -2][ T -1]

Tardigrade Admin · Accepted Answer

Dimensional formula of energy [E]=[M1 L2 T-2] ldots(I) Dimensional formula of gravitational constant [G]=[M-1 L3 T-2] ldots text (II) Dividing (I) by (II), we get: Hence, E / G==[M2 L-1 T0]

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

$[M^{2}] [L^{- 1}] [T^{0}]$

$[M] [L^{- 1}] [T^{- 1}]$

$[M] [L^{0}] [T^{0}]$

$[M^{2}] [L^{- 2}] [T^{- 1}]$

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

Q. If E and G respectively denote energy and gravitational constant, then GE​ has the dimensions of:

[M2][L−1][T0]

[M][L−1][T−1]

[M][L0][T0]

[M2][L−2][T−1]