NEETPhysicsUnits and Dimensions
Match List-I with List-II. List-I List-II (A) Planck Length (I) c^ 1/2 G^ -1/2 h^ 1/2 (B) Planck Mass (II) c^ -3/2 G^ 1/2 h^ 1/2 (C) Planck Time (III) c^ 5/2 G^ -1/2 h^ 1/2 (D) Planck Energy (IV) c^ -5/2 G^ 1/2 h^ 1/2 Choose the correct answer from the options given below:
Options
- A(A)-(IV), (B)-(I), (C)-(II), (D)-(III)
- B(A)-(II), (B)-(III), (C)-(IV), (D)-(I)
- C(A)-(II), (B)-(I), (C)-(IV), (D)-(III)
- D(A)-(I), (B)-(II), (C)-(III), (D)-(IV)
Correct answer
C. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
Step-by-step solution
First, write the dimensional formulas for the fundamental constants: Speed of light, [c] = [L T⁻¹] Universal gravitational constant, [G] = [M⁻¹ L^3 T⁻²] Planck's constant, [h] = [M L^2 T⁻¹] Let us evaluate the common term G^ 1/2 h^ 1/2 : [G h]^ 1/2 = (M⁻¹ L^3 T⁻² M L^2 T⁻¹)^ 1/2 = (L^5 T⁻³)^ 1/2 = [L^ 5/2 T^ -3/2 ] To obtain Planck Length [L^1] , we need to multiply by a power of c that yields L^1 T^0 . Multiplying by c^ -3/2 = (L T⁻¹)^ -3/2 = L^ -3/2 T^ 3/2 gives: L^ 5/2 T^ -3/2 L^ -3/2 T^ 3/2 = [L^1] . Thus, Plan