Which of the following statements is correct based on dimensional analysis?

• A. Multiplying a quantity in meters by a quantity in seconds yields a result with units of meter-seconds (m·s).
• B. Subtracting a quantity in liters from a quantity in grams is valid if both quantities are positive.
• C. Dividing a quantity in joules by a quantity in seconds gives a result with units of meters.
• D. Adding a quantity in kilograms to a quantity in meters is valid because both are SI units.

Answer: (A)

Verified step by step guidance

1. Step 1: Understand the principle of dimensional analysis, which states that only quantities with the same units can be added or subtracted, while multiplication and division combine units algebraically.
2. Step 2: Analyze the first statement: Multiplying meters (m) by seconds (s) results in units of meter-seconds (m·s), which is valid because multiplication combines units by placing them together.
3. Step 3: Analyze the second statement: Subtracting liters (L) from grams (g) is invalid because these units measure different physical quantities (volume vs. mass) and cannot be directly subtracted regardless of their positivity.
4. Step 4: Analyze the third statement: Dividing joules (J) by seconds (s) does not yield meters (m). Since joule is a unit of energy (kg·m²/s²), dividing by seconds results in watts (J/s = W), a unit of power, not length.
5. Step 5: Analyze the fourth statement: Adding kilograms (kg) to meters (m) is invalid because they represent different physical quantities (mass vs. length), even though both are SI units; addition requires the same units.