Match Column-I with Column-II. [PMT/NEET-2022]

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Column–I	Column–II
(A) Gravitational constant (G)	1. $[L^{2} T^{-2}]$
(B) Gravitational potential energy	2. $[M^{-1} L^{3} T^{-2}]$
(C) Gravitational potential	3. $[L T^{-2}]$
(D) Gravitational intensity	4. $[M L^{2} T^{-2}]$

Choose the correct answer from the options given below:
a. A → 2; B → 1; C → 4; D → 3
b. A → 2; B → 4; C → 1; D → 3
c. A → 2; B → 4; C → 3; D → 1
d. A → 4; B → 2; C → 1; D → 3

Answer: b. A → 2; B → 4; C → 1; D → 3

Explanation:
Let me find the dimensions of each gravitational quantity systematically and match them with the given options.

(A) Gravitational Constant (G)

From Newton’s law of gravitation: $ F = \frac{Gm_1m_2}{r^2} $

Rearranging: $ G = \frac{Fr^2}{m_1m_2} $

Force F: $ [MLT^{-2}] $
Distance squared r²: $ [L^2] $
Product of masses: $ [M^2] $

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

A matches with 2

(B) Gravitational Potential Energy

Gravitational potential energy is a form of energy, so it has the standard energy dimensions:
$
[PE] = [ML^2T^{-2}] $

B matches with 4

(C) Gravitational Potential

Gravitational potential is defined as gravitational potential energy per unit mass:
$ \text{Potential} = \frac{\text{Potential Energy}}{\text{Mass}} $

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

C matches with 1

(D) Gravitational Intensity (Gravitational Field)

Gravitational intensity is the same as gravitational acceleration:
$
[g] = [LT^{-2}] $

D matches with 3

Final Matching