JEE MAIN - Physics (2025 - 3rd April Morning Shift - No. 6)

$$ \text { Match the LIST-I with LIST-II } $$

List - I		List - II
A.	$$ \text { Gravitational constant } $$	I.	$$ \left[\mathrm{LT}^{-2}\right] $$
B.	$$ \text { Gravitational potential energy } $$	II.	$$ \left[\mathrm{L}^2 \mathrm{~T}^{-2}\right] $$
C.	$$ \text { Gravitational potential } $$	III.	$$ \left[\mathrm{ML}^2 \mathrm{~T}^{-2}\right] $$
D.	$$ \text { Acceleration due to gravity } $$	IV.	$$ \left[\mathrm{M}^{-1} \mathrm{~L}^3 \mathrm{~T}^{-2}\right] $$

Choose the correct answer from the options given below:

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

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

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

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

Here’s how each quantity lines up with its dimensional formula:

Gravitational constant, $$G$$

• From Newton’s law $$F = G\frac{m_1m_2}{r^2}$$

• $$[G] = \frac{[F]\,[r]^2}{[m]^2} = \frac{(MLT^{-2})\;L^2}{M^2} = M^{-1}L^3T^{-2}$$

⇒ IV

Gravitational potential energy, $$U$$

• As work or $$U = mgh$$

• $$[U] = [F]\,[h] = (MLT^{-2})\;L = ML^2T^{-2}$$

⇒ III

Gravitational potential, $$\phi$$

• Energy per unit mass: $$\phi = \frac{U}{m}$$

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

⇒ II

Acceleration due to gravity, $$g$$

• Just an acceleration

• $$[g] = LT^{-2}$$

⇒ I

Matching them gives

A–IV, B–III, C–II, D–I

That corresponds to Option A.