Consider two physical quantities A and B related to each other as E = (B - x²)/(At), where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is
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Question

Consider two physical quantities A and B related to each other as E = (B - x²)/(At), where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

G1 Physics · Accepted Answer

Since B and x² are subtracted: [B] = [x²] = L² From: E = (B - x²)/(At) [A] = [B]/([t][E]) = L²/[T × (ML²T⁻²)] = M⁻¹T Therefore, [AB] = (M⁻¹T)(L²) = L²M⁻¹T