Question

Work done=?

• A. Force $\times$ Distance
• B. Mass $\times$ Velocity
• C. Power $\times$ Time
• D. Force $\times$ Acceleration

Hint:

Always remember: No movement = No work. You can push against a brick wall all day and feel tired, but in the eyes of physics, if the wall didn't move any distance, you did zero Joules of work.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
The question asks for the fundamental formula that defines the concept of "Work" in classical physics.
Step 2: Key Formula or Approach:
The physics formula for work is more completely expressed as:
\[ W = F \cdot d \cdot \cos(\theta) \]
Here, \( F \) is the magnitude of the force, \( d \) is the magnitude of the displacement (distance), and \( \theta \) is the angle between the force vector and the displacement vector.
Step 3: Detailed Explanation:

• Core Definition: In physics, "work" is performed on an object only when an applied force causes it to move through a distance. If the object does not move, no work is done in the physical sense, no matter how great the force.
  
• Standard Case: For many simple problems, the force is applied in the same direction as the object's motion. In this case, the angle \( \theta \) is $0^{\circ}$, and since \( \cos(0^{\circ}) = 1 \), the formula simplifies to \( \text{Work} = \text{Force} \times \text{Distance} \). This is the relationship presented in option (A).
  
• Evaluating Alternatives:
  - Mass $\times$ Velocity (B): This is the formula for linear momentum (\( p = mv \)).
  - Power $\times$ Time (C): This calculation also equals work (\( W = P \times t \)), as power is the rate of doing work. However, Force $\times$ Distance is the more primary definition of work itself.
  - Force $\times$ Acceleration (D): This product does not correspond to a standard physical quantity. (Force is equal to mass $\times$ acceleration).
  
• Units of Work: The SI unit for work is the Joule (J). One Joule is defined as the work done by a force of one Newton acting over a distance of one meter.
  

Step 4: Final Answer:
The most fundamental definition of work provided among the choices is the product of Force and Distance.

Answer 2

Since work is measured in Joules, with base units \( \text{kg}\cdot\text{m}^2/\text{s}^2 \), checking which product of quantities among the options actually reduces to those units settles the question.

1. Force \(\times\) Distance: Force has units \( \text{kg}\cdot\text{m}/\text{s}^2 \) and distance has units \( \text{m} \). Multiplying gives \( \text{kg}\cdot\text{m}^2/\text{s}^2 \), which matches the Joule exactly.
2. Mass \(\times\) Velocity: Mass has units \( \text{kg} \) and velocity has units \( \text{m/s} \). Multiplying gives \( \text{kg}\cdot\text{m/s} \), the units of momentum, not work.
3. Power \(\times\) Time: Power has units \( \text{kg}\cdot\text{m}^2/\text{s}^3 \) and time has units \( \text{s} \). Multiplying gives \( \text{kg}\cdot\text{m}^2/\text{s}^2 \), which also reduces to Joules; this option is dimensionally valid too, since power is itself defined as work per unit time, so multiplying back by time recovers work. However, it describes work only indirectly, through a rate, rather than through the primary force-and-displacement definition being asked for here.
4. Force \(\times\) Acceleration: Force has units \( \text{kg}\cdot\text{m}/\text{s}^2 \) and acceleration has units \( \text{m}/\text{s}^2 \). Multiplying gives \( \text{kg}\cdot\text{m}^2/\text{s}^4 \), which does not match the units of work at all, and does not correspond to any standard named physical quantity.

The most direct, foundational match, both dimensionally and conceptually, for the definition of work is force multiplied by the distance moved.

Therefore, the correct answer is Force \(\times\) Distance.