A wooden door is 1 m wide, 2.5 m tall, 6 cm thick, and weighs 400 N. What is the density of the wood in g/cm³? (use g = 10 m/s²)

• A. 0.0267 g/cm³
• B. 0.267 g/cm³
• C. 267 g/cm³
• D. 2670 g/cm³

Answer: (B)

Verified step by step guidance

1. First, calculate the volume of the door. The volume V can be found using the formula V = width × height × thickness. Convert all dimensions to meters: width = 1 m, height = 2.5 m, thickness = 0.06 m.
2. Substitute the values into the volume formula: V = 1 m × 2.5 m × 0.06 m.
3. Next, calculate the mass of the door. Use the weight of the door and the acceleration due to gravity. The weight W is given as 400 N, and g = 10 m/s². Use the formula W = m × g to find the mass m.
4. Rearrange the formula to solve for mass: m = W / g. Substitute the given values: m = 400 N / 10 m/s².
5. Finally, calculate the density of the wood. Density ρ is mass divided by volume, ρ = m / V. Convert the density from kg/m³ to g/cm³ by multiplying by 1000 (since 1 kg/m³ = 0.001 g/cm³).