The dimensions of universal gravitational constant are:

The dimensions of universal gravitational constant are:
  1. $\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$
  2. $\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]$
  3. $\left[\mathrm{ML}^{-2} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]$
  4. $\left[\mathrm{ML}^{-2} \mathrm{~L}^2 \mathrm{~T}^{-1}\right]$

Solution

$\begin{aligned} F & =\frac{\mathrm{GMm}}{R^2} \\ \Rightarrow \mathrm{G}=\frac{F R^2}{M m} & =\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^2\right]}{\left[\mathrm{M}^2\right]} \\ & =\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] \end{aligned}$

Asked in: NEET 2004

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