The unit of work, joule, is dimensionally the same as:Select one:a.newton/kilogram.b.newton-meter.c.newton-second.d.newton/sec

To determine the unit of work, joule, and find the dimensionally equivalent option, let's analyze the options provided.

Break Down the Problem

1. Understand the unit of work (joule): The joule (J) is defined as the amount of work done when a force of one newton displaces an object by one meter in the direction of the force.
2. Identify components: A joule can be expressed in terms of newtons and meters.

Relevant Concepts

• Definition of a joule: $1 \, \text{J} = 1 \, \text{N} \cdot 1 \, \text{m}$
• Newtons are defined as: $1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2$

Analysis and Detail

• Considering the unit of work: $1 \, \text{J} = 1 \, \text{N} \cdot 1 \, \text{m} = (1 \, \text{kg} \cdot \text{m/s}^2) \cdot (1 \, \text{m}) = 1 \, \text{kg} \cdot \text{m}^2/\text{s}^2$

• Now let's analyze the options:

  1. a. newton/kilogram: This does not simplify correctly to joules.
  2. b. newton-meter: This simplifies directly to joules since $1 \, \text{N} \cdot 1 \, \text{m} = 1 \, \text{J}$.
  3. c. newton-second: This represents momentum, not work.
  4. d. newton/sec: This has dimensions of force per time, relating to rates of change.

Verify and Summarize

By summarizing, we see that only option b (newton-meter) equates dimensionally to joules.

Final Answer

The unit of work, joule, is dimensionally the same as b. newton-meter.