The dimensions of universal gravitational constant are: [PMT/NEET-2004]
a. $[M^{-1}L^{3}T^{-2}]$
b. $[ML^{2}T^{-1}]$
c. $[M^{-2}L^{3}T^{-2}]$
d. $[M^{-2}L^{2}T^{-1}]$

Answer: a. $ [M^{-1}L^{3}T^{-2}] $

Explanation:
Newton’s law of gravitation is $ F = \dfrac{G\,m_1 m_2}{r^{2}} $.

Solving for the gravitational constant, $ G = \dfrac{F\,r^{2}}{m_1 m_2} $.

• Force has dimensions $ [M L T^{-2}] $.
• Distance squared contributes $ [L^{2}] $.
• The product of the two masses gives $ [M^{2}] $.

Combining these, the dimensional formula for $ G $ is
$
[M L T^{-2}] [L^{2}] [M^{2}]^{-1} = M^{1-2} L^{1+2} T^{-2} = M^{-1} L^{3} T^{-2} $.

Hence, option a is correct.