Which of the following is equivalent to 1 N·m in terms of SI base units?

• A. 1 kg·m·s^{-1}
• B. 1 kg·m·s^{-2}
• C. 1 kg·m^2·s^{-2}
• D. 1 kg·m^2·s^{-1}

Answer: (C)

Verified step by step guidance

1. Recall that 1 N (newton) is defined as the force required to accelerate 1 kg of mass at 1 m/s². In SI base units, 1 N = 1 kg·m·s^{-2}.
2. Understand that 1 N·m (newton meter) is a unit of torque or work, which is force multiplied by distance. So, 1 N·m = (1 N) × (1 m).
3. Substitute the base unit expression for newton into the equation: 1 N·m = (1 kg·m·s^{-2}) × (1 m).
4. Multiply the units together by combining like terms: kg·m·s^{-2} × m = kg·m^{2}·s^{-2}.
5. Conclude that 1 N·m expressed in SI base units is equivalent to 1 kg·m^{2}·s^{-2}.