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NEET 2004
Exam
NEET
Year
2004
Subject
Physics
Chapter
Units and Dimensions

NEET 2004 · Physics · Units and Dimensions

The dimensions of universal gravitational constant are:

The dimensions of universal gravitational constant are:

Options

  1. A[M−1 L3 T−2]\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]
  2. B[ML2 T−1]\left[\mathrm{ML}^2 \mathrm{~T}^{-1}\right]
  3. C[ML−2 L3 T−2]\left[\mathrm{ML}^{-2} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]
  4. D[ML−2 L2 T−1]\left[\mathrm{ML}^{-2} \mathrm{~L}^2 \mathrm{~T}^{-1}\right]

Correct answer

A. [M−1 L3 T−2]\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]

Step-by-step solution

F=GMmR2⇒G=FR2Mm=[MLT−2][L2][M2]=[M−1 L3 T−2]\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}
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