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JEE Mains · Physics · STD 11 - Units,dimensions and measurement
  • JEE Mains 2025
  • Medium
  • MCQ

Match the LIST-I with LIST-II
LIST-ILIST-II
(A) Gravitational constant(I) \(\left[\mathrm{LT}^{-2}\right]\)
(B) Gravitational potential energy(II) \(\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]\)
(C) Gravitational potential(III) \(\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]\)
(D) Acceleration due to gravity(IV) \(\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\)
Choose the correct answer from the options given below :

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Verified Solution

Answer & Solution

Correct Answer

(A) A-IV, B-III, C-II, D-I

Step-by-step Solution

Detailed explanation

\(\begin{aligned}
& \text { (A) } \mathrm{G}=\frac{\mathrm{Fr}^2}{\mathrm{~m}^2} \\
& {[\mathrm{G}]=\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^2\right]}{\left[\mathrm{M}^2\right]}=\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right](\mathrm{IV})}
\end{aligned}\)
(B)
\(\begin{aligned}
& \text { P.E. }=\mathrm{mgh}=\left[\mathrm{MLT}^{-2} \mathrm{~L}\right] \\
& =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] \text { (III) }
\end{aligned}\)
(C) Gravitational Potential \(=\frac{\mathrm{GM}}{\mathrm{r}}\)
\(=\frac{\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right][\mathrm{M}]}{[\mathrm{L}]}=\left[\mathrm{M}^0 \mathrm{~L}^2 \mathrm{~T}^{-2}\right]=\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right](\mathrm{II})\)
(D) Acceleration due to gravity \(=[\mathrm{g}]=\left[\mathrm{LT}^{-2}\right](\mathrm{I})\)
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