The dimensional formula for the gravitational constant is:

Question

The dimensional formula for the gravitational constant is: (A)  text ! ![ ! ! text textM text-1 textL text3 textT text-2 text ! !] ! ! text  (B)  text ! ![ ! ! text ML textT text-2 text ! !] ! ! text  (C)  text ! ![ ! ! text M textL2 textT-2 text ! !] ! ! text  (D)  text ! ![ ! ! text textM-1 textL3 textT ! !] ! ! text

Tardigrade Admin · Accepted Answer

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 apart.

∴

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

(Newtons law of gravitation) where

m_{1}

and

m_{2}

are masses, r is the distance between them, and F is force.

∴

Dimensions of gravitational constant

= \frac{dimensions of force \times (length) ^{2}}{(dimensions of mass) ^{2}}

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

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

Q. The dimensional formula for the gravitational constant is:

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

$[ML T^{-2}]$

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

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

Q. The dimensional formula for the gravitational constant is:

[M-1L3T-2]

[ MLT-2]

[ ML2T−2]

[M−1L3T ]

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

$[ML T^{-2}]$

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

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