2004 AIPMT Units and MeasurementsDimensional Formula Easy Question 51 of 53 in Units and Measurements

The dimensions of universal gravitational constant are :-

A $ML^2T^{-1}$
B $M^{-2}L^3T^{-2}$
C $M^{-2}L^2T^{-1}$
D $M^{-1}L^3T^{-2}$

The answer is D.

Solution

Newton's law of gravitation: $F = \dfrac{Gm_1m_2}{r^2}$
$\therefore G = \dfrac{Fr^2}{m_1m_2}$
$[G] = \dfrac{[F][r^2]}{[m^2]} = \dfrac{MLT^{-2} \cdot L^2}{M^2}$
$= M^{-1}L^3T^{-2}$
So the dimensions of the universal gravitational constant are $M^{-1}L^3T^{-2}$.

Concept Dimensions of G

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53 questions from this chapter have appeared across 25 exam years.