Q72 / 75 · JEE Main 2025 (3 Apr Shift 1) · Physics
Match the LIST-I with LIST-II
$\begin{array}{|l|l|l|l|}\hline & \text{LIST-I} & & \text{LIST-II} \\ \hline \text{A.} & \text{Gravitational constant} & \text{I.} & {\left[\mathrm{LT}^{-2}\right]} \\ \hline \text{B.} & \begin{array}{l} \text{Gravitational potential} \\ \text{energy} \end{array} & \text{II.} & {\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]} \\ \hline \text{C.} & \text{Gravitational potential} & \text{III.} & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]} \\ \hline \text{D.} & \begin{array}{l} \text{Acceleration due to} \\ \text{gravity} \end{array} & \text{IV.} & {\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]} \\ \hline \end{array}$
Choose the correct answer from the options given below :
$\begin{array}{|l|l|l|l|}\hline & \text{LIST-I} & & \text{LIST-II} \\ \hline \text{A.} & \text{Gravitational constant} & \text{I.} & {\left[\mathrm{LT}^{-2}\right]} \\ \hline \text{B.} & \begin{array}{l} \text{Gravitational potential} \\ \text{energy} \end{array} & \text{II.} & {\left[\mathrm{L}^2 \mathrm{~T}^{-2}\right]} \\ \hline \text{C.} & \text{Gravitational potential} & \text{III.} & {\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right]} \\ \hline \text{D.} & \begin{array}{l} \text{Acceleration due to} \\ \text{gravity} \end{array} & \text{IV.} & {\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]} \\ \hline \end{array}$
Choose the correct answer from the options given below :
- Correct answerAA-IV, B-III, C-II, D-I
- BA-III, B-II, C-I, D-IV
- CA-II, B-IV, C-III, D-I
- DA-I, B-III, C-IV, D-II
Solution
$\begin{aligned}<br/>& \text { (A) } \mathrm{G}=\frac{\mathrm{Fr}^2}{\mathrm{~m}^2} \\
& {[\mathrm{G}]=\frac{\left[\mathrm{MLT}^{-2}\right]\left[\mathrm{L}^2\right]}{\left[\mathrm{M}^2\right]}=\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right](\mathrm{IV})}<br/>\end{aligned}$
(B)
$\begin{aligned}<br/>& \text { P.E. }=\mathrm{mgh}=\left[\mathrm{MLT}^{-2} \mathrm{~L}\right] \\ & =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] \text { (III) }<br/>\end{aligned}$
(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 $=[\mathrm{g}]=\left[\mathrm{LT}^{-2}\right](\mathrm{I})$
(B)
$\begin{aligned}<br/>& \text { P.E. }=\mathrm{mgh}=\left[\mathrm{MLT}^{-2} \mathrm{~L}\right] \\ & =\left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] \text { (III) }<br/>\end{aligned}$
(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 $=[\mathrm{g}]=\left[\mathrm{LT}^{-2}\right](\mathrm{I})$
Hence, the correct answer is option: 'A'.