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Dimensional Analysis

Question

The dimension of universal gravitational constant is :
$[M^{- 2} L^{- 3} T^{- 2}]$
$[M^{- 2} L^{2} T^{- 1}]$
$[M^{- 1} L^{3} T^{- 2}]$
$[M L^{2} T^{- 1}]$

A

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

B

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

C

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

D

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

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Solution

Verified by Toppr

The correct option is C $[M^{- 1} L^{3} T^{- 2}]$
$F = \frac{G m_{1} m_{2}}{r^{2}}$
$\Rightarrow G = \frac{F r^{2}}{m_{1} m_{2}} = \frac{[M L T^{- 2}] [L^{2}]}{[M^{2}]}$
$= [M^{- 1} L^{3} T^{- 2}]$ .

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