JEE Mains · Physics · STD 11 - Units,dimensions and measurement
- JEE Mains 2025
- Medium
- MCQ
Match the LIST-I with LIST-II
| LIST-I | LIST-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) \(\left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right]\) |
Pick an option to check your answer.
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 \(=[\mathrm{g}]=\left[\mathrm{LT}^{-2}\right](\mathrm{I})\)
& \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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