CMS Dimensional Analysis & Metric Calculations 2 — Questions and Answers
Question 1: Which of the following correctly applies the chain rule of dimensional analysis to convert 60 miles per hour to km/h? (1 mile = 1.609 km)
- 60 × 1.609 = 96.54 km/h (Correct answer)
- 60 ÷ 1.609 = 37.3 km/h
- 60 × 0.621 = 37.3 km/h
- 60 ÷ 0.621 = 96.6 km/h
Correct answer: 60 × 1.609 = 96.54 km/h
60 mi/h × 1.609 km/mi = 96.54 km/h; multiply by the conversion factor to go from smaller to larger.
Question 2: A room has dimensions 4 m × 5 m × 3 m. What is its volume in cubic metres?
- 12 m³
- 47 m³
- 60 m³ (Correct answer)
- 120 m³
Correct answer: 60 m³
Volume = length × width × height = 4 × 5 × 3 = 60 m³.
Question 3: The density of water is 1,000 kg/m³. What is this in g/cm³?
- 0.001 g/cm³
- 0.1 g/cm³
- 1 g/cm³ (Correct answer)
- 100 g/cm³
Correct answer: 1 g/cm³
1,000 kg/m³ = 1 g/cm³, since 1 kg = 1,000 g and 1 m³ = 1,000,000 cm³, giving 1,000,000/1,000,000 = 1 g/cm³.
Question 4: Convert 25°C to Kelvin:
- 248 K
- 298 K (Correct answer)
- 273 K
- 25 K
Correct answer: 298 K
K = °C + 273.15, so 25 + 273.15 ≈ 298 K (rounded to 298 K).
Question 5: Power is defined as energy per unit time. If 600 J of work is done in 0.5 minutes, what is the power in watts?
- 20 W
- 1,200 W (Correct answer)
- 300 W
- 20 W
Correct answer: 1,200 W
Power = 600 J ÷ (0.5 × 60 s) = 600 ÷ 30 = 20 W.
Question 6: A 50 kg object is accelerated at 2 m/s². What force is applied in newtons?
- 25 N
- 52 N
- 100 N (Correct answer)
- 1,000 N
Correct answer: 100 N
F = ma = 50 kg × 2 m/s² = 100 N.
CMS Dimensional Analysis & Metric Calculations 2
Which of the following correctly applies the chain rule of dimensional analysis to convert 60 miles per hour to km/h? (1 mile = 1.609 km)