Match the LIST-I with LIST-II LIST-I A. Gravitational constant B. Gravitational potential energy C. Gravitational potential D. Acceleration due to gravity LIST-II I. [LT-2] II. [L2T-2] III. [ML2T-2] IV. [M-1L3T-2] Choose the correct answer from the options given below:

The correct answer is Option 1. Full mathematical solution steps and hints are accessible in the interactive StemCET workspace.

Physics Q27 – JEE-MAIN 2025

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Home Physics GravitationQuestion #196

Match the LIST-I with LIST-II

\begin{array}{lcl} 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}] \end{array}

Choose the correct answer from the options given below:

Clue 1 of 3: Recall the fundamental definitions and formulas for each physical quantity listed

Dimensions are derived from these definitions.

🥷

Ninja Strategy•Anchor Point Elimination

Start with the most commonly known dimensions, like acceleration due to gravity (D), to eliminate options quickly. Then, verify another quantity like the gravitational constant (A) to pinpoint the correct answer.

🧠 Full Solution Path

Step 1: Determine Dimensions for Each Quantity✦ Active

We will derive the dimensions for each quantity in List-I:

A. Gravitational constant (G):

F = G \frac{m_{1} m_{2}}{r^{2}} ⟹ G = \frac{F r^{2}}{m_{1} m_{2}}

[G] = \frac{[M L T^{- 2}] [L^{2}]}{[M^{2}]} = [M^{- 1} L^{3} T^{- 2}]

(Matches IV)

B. Gravitational potential energy (U):

Energy has dimensions of work:

U = F \cdot d

[U] = [M L T^{- 2}] [L] = [M L^{2} T^{- 2}]

(Matches III)

C. Gravitational potential (V):

Potential is energy per unit mass:

V = \frac{U}{m}

[V] = \frac{[M L^{2} T^{- 2}]}{[M]} = [L^{2} T^{- 2}]

(Matches II)

D. Acceleration due to gravity (g):

Acceleration has dimensions of

[L T^{- 2}]

(Matches I)

Step 2: Match List-I with List-II○ Expand

Based on the derived dimensions, we form the following matches:

\to

IV B

\to

III C

\to

II D

\to

Step 3: Select the Correct Option○ Expand

Comparing these matches with the given options, option 1 (A-IV, B-III, C-II, D-I) is the correct choice.

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Physics Question 27 – JEE-MAIN 2025

Clue 1 of 3: Recall the fundamental definitions and formulas for each physical quantity listed

🧠 Full Solution Path