Question Detail
Question
Suppose A = Bⁿ Cᵐ, where A has dimensions LT⁻², B has dimensions LT⁻¹, and C has dimensions LT². Then the exponents n and m have the values:
Correct Answer
Option A is the correct answer.
Detailed Explanation
Dimensions: [A] = [B]ⁿ [C]ᵐ = (LT⁻¹)ⁿ (LT²)ᵐ = Lⁿ⁺ᵐ T⁻ⁿ⁺²ᵐ. Equate to LT⁻²: L: n + m = 1; T: -n + 2m = -2. Solve: add equations: (n+m) + (-n+2m) = 1 + (-2) → 3m = -1 → m = -1/3. Then n = 1 - m = 1 + 1/3 = 4/3. Not matching options. If A = LT⁻², B = LT⁻¹, C = LT², then n+m=1, -n+2m=-2 → multiply first by 2: 2n+2m=2, add to second? Actually solve: from first, n=1-m. Substitute: -(1-m)+2m=-2 → -1+m+2m=-2 → 3m = -1 → m=-1/3, n=4/3. None match. Option A is 2/3, 1/3, sum=1, but T: -2/3 + 2/3 = 0, not -2. So not correct.
Hint
Set up dimensional equations and solve.