Question

Choose the correct answer from the options given below:

List – I	List – II
(a) Gravitational constant	(i) [L2T-2]
(b) Gravitational potential energy	(ii) [M-1L3T-2]
(c) Gravitational potential	(iii) [LT-2]
(d) Gravitational intensity	(iv) [ML2T-2

• (a) - (ii), (b) - (i), (c)-(iv), (d) - (iii)
• (a) - (ii), (b) - (iv), (c)-(i), (d) - (iii)
• (a) - (ii), (b) - (iv), (c)-(iii), (d) - (i)
• (a) - (iv), (b) - (ii), (c)-(i), (d) - (iii)

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
Physical quantities related to gravitation can be analyzed through dimensional formulas derived from their definitions.
Step 2: Detailed Explanation:
1. Gravitational constant (G):
From Newton's law: \(F = \frac{G m_1 m_2}{r^2} \implies G = \frac{F r^2}{m^2}\).
\[ [G] = \frac{[MLT^{-2}][L^2]}{[M^2]} = [M^{-1}L^3T^{-2}] \quad \rightarrow \text{Matches (ii)} \]
2. Gravitational potential energy:
Energy of any form has dimensions of Work:
\[ \text{Work} = \text{Force} \times \text{Distance} = [MLT^{-2}][L] = [ML^2T^{-2}] \quad \rightarrow \text{Matches (iv)} \]
3. Gravitational potential:
Potential is defined as Potential Energy per unit mass:
\[ V = \frac{U}{m} = \frac{[ML^2T^{-2}]}{[M]} = [L^2T^{-2}] \quad \rightarrow \text{Matches (i)} \]
4. Gravitational intensity:
Intensity is the gravitational force per unit mass (acceleration due to gravity):
\[ I = \frac{F}{m} = \frac{[MLT^{-2}]}{[M]} = [LT^{-2}] \quad \rightarrow \text{Matches (iii)} \]
Step 3: Final Answer:
Matching the lists: (a)-(ii), (b)-(iv), (c)-(i), (d)-(iii).