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Physical quantities A, B, C, D, E, F, G, H, I, J, K are related by the equation A = B/C + (D + E)/F + G*(H - I)/(J + K). Which of the following statements about their dimensions are correct? (Select all that apply.)

1. [A] = [B/C]
2. [A] = [G*I/K]
3. [D/F] = [G*H/J]
4. [BC] = [G/K]

Correct answer: [A] = [B/C]

Solution

Each term in the sum has dimension [A], so [B/C]=[A] (option A, TRUE), and [G*I/K]=[G*(H-I)/(J+K)]=[A] (option B, TRUE), and [D/F]=[G*H/J]=[A] (option C, TRUE); option D claims [BC]=[G/K] but [B]=[A][C] so [BC]=[A][C²] while [G/K]=[A][J/H], which are not equal in general (FALSE).

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