JEE Main 2025 — Gravitation Question with Solution

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

Gravitational constant, $$G$$

• From Newton’s law $$F=G\frac{m_1{m}_2}{r^2}$$

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

⇒ IV

Gravitational potential energy, $$U$$

• As work or $$U=mgh$$

• $$[U]=[F][h]=(ML{T}^{-2})L=M{L}^2{T}^{-2}$$

⇒ III

Gravitational potential, $$\varphi$$

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

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

⇒ II

Acceleration due to gravity, $$g$$

• Just an acceleration

• $$[g]=L{T}^{-2}$$

⇒ I

Matching them gives

A–IV, B–III, C–II, D–I

That corresponds to Option A.