JEE Main 2025 Apr 3 Shift 1, Physics Q9: Units And Dimensions

JEE Main2025Apr 3, Shift 1Physics

Match the LIST-I with LIST-II

LIST-I	LIST-II
A. Gravitational constant	I. $[L T^{- 2}]$
B. Gravitational potential energy	II. $[L^{2} T^{- 2}]$
C. Gravitational potential	III. $[M L^{2} T^{- 2}]$
D. Acceleration due to gravity	IV. $[M^{- 1} L^{3} T^{- 2}]$

Choose the correct answer from the options given below :

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

Solution

Dimensional analysis for each entry in LIST-I:

A. Gravitational constant $G$ : From $F = \frac{G m _{1} m _{2}}{r ^{2}}$ , $[G] = \frac{[ F ] [ L ^{2} ]}{[ M ^{2} ]} = \frac{[ M L T ^{- 2} ] [ L ^{2} ]}{[ M ^{2} ]} = [M^{- 1} L^{3} T^{- 2}]$ → IV.

B. Gravitational PE = $m g h$ : $[M] [L T^{- 2}] [L] = [M L^{2} T^{- 2}]$ → III.

C. Gravitational potential $V = \frac{GM}{r}$ : $\frac{[ M ^{- 1} L ^{3} T ^{- 2} ] [ M ]}{[ L ]} = [L^{2} T^{- 2}]$ → II.

D. $g$ : $[L T^{- 2}]$ → I.

$∴$ A-IV, B-III, C-II, D-I.

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JEE Main 2025 Apr 3 Shift 1, Physics Q9: Units And Dimensions

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