The dimensions of gravitational constant G are:

Question

The dimensions of gravitational constant G are: (A) [ ML 3 T -2] (B) [ M -1 L 2 T -2] (C) [ ML -2 T -2] (D) [ M -1 L 3 T -2]

Tardigrade Admin · Accepted Answer

Key Idea: From definition, gravitational constant is equal in magnitude to that force of attraction which acts between two particles each of unit mass separated by a unit distance.
Numerically, gravitational constant

G = \frac{F r ^{2}}{m _{1} m _{2}}

where F is force, r is the distance between the two masses

m_{1}

and

m_{2} . < b r >< b r >

Writing the dimensions of all the quantities in the above formula, the dimensions of G are

[G] = \frac{[ M L T ^{- 2} ] [ L ^{2} ]}{[ M ] [ M ]} = [M^{- 1} L^{3} T^{- 2}]

Q. The dimensions of gravitational constant G are:

$[M L^{3} T^{- 2}]$

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

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

$[M^{- 1} L^{3} T^{- 2}]$

Q. The dimensions of gravitational constant G are:

[ML3T−2]

[M−1L2T−2]

[ML−2T−2]

[M−1L3T−2]

$[M L^{3} T^{- 2}]$

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

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

$[M^{- 1} L^{3} T^{- 2}]$