Match List-I with List-II:

**List-I**
(a) Gravitational constant (G)
(b) Gravitational potential energy
(c) G

Question

Match List-I with List-II:

**List-I**
(a) Gravitational constant (G)
(b) Gravitational potential energy
(c) Gravitational potential
(d) Gravitational intensity

**List-II**
(i) $[L^2 T^{-2}]$
(ii) $[M^{-1} L^3 T^{-2}]$
(iii) $[LT^{-2}]$
(iv) $[ML^2 T^{-2}]$

Choose the correct answer from the options given below:

Accepted Answer

1. **Gravitational Constant ($G$):** From the formula $F = \frac{Gm_1m_2}{r^2}$, we have $G = \frac{Fr^2}{m_1m_2}$. The dimensions are $\frac{[MLT^{-2}][L^2]}{[M][M]} = [M^{-1}L^3T^{-2}]$. This matches **(ii)**.
2. **Gravitational Potential Energy ($U$):** Energy has the same dimensions as Work ($F \cdot d$). The dimensions are $[MLT^{-2}][L] = [ML^2T^{-2}]$. This matches **(iv)**.
3. **Gravitational Potential ($V$):** Potential is defined as potential energy per unit mass ($V = U/m$). The dimensions are $\frac{[ML^2T^{-2}]}{[M]} = [L^2T^{-2}]$. This matches **(i)**.
4. **Gravitational Intensity ($E$ or $g$):** This is the gravitational force per unit mass (acceleration due to gravity). The dimensions are $\frac{[MLT^{-2}]}{[M]} = [LT^{-2}]$. This matches **(iii)**.

Therefore, the correct matching is (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii).

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