Which one has the dimensions different from the remaining three

A. power
B. work
C. torque
D. energy

Options

A. power
B. Work
C. torque
D. energy

Answer

To determine which of the options has dimensions different from the remaining three, we will analyze the dimensions of power, work, torque, and energy step by step.

### Step 1: Analyze the dimensions of power
Power (P) is defined as the rate at which work is done. The formula for power is:
\[ P = \frac{W}{t} \]
Where:
- \( W \) is work
- \( t \) is time

The dimensions of work (W) can be expressed as:
\[ W = \text{Force} \times \text{Distance} \]
Force (F) has the dimensions:
\[ F = MLT^{-2} \]
Distance (D) has the dimensions:
\[ D = L \]
Thus, the dimensions of work are:
\[ W = MLT^{-2} \cdot L = ML^2T^{-2} \]

Now substituting this into the power formula:
\[ P = \frac{ML^2T^{-2}}{T} = ML^2T^{-3} \]

### Step 2: Analyze the dimensions of work
As derived above, the dimensions of work are:
\[ W = ML^2T^{-2} \]

### Step 3: Analyze the dimensions of torque
Torque (τ) is defined as:
\[ τ = \text{Force} \times \text{Distance} \]
Using the dimensions of force:
\[ τ = MLT^{-2} \cdot L = ML^2T^{-2} \]

### Step 4: Analyze the dimensions of energy
Energy has the same dimensions as work. Thus:
\[ E = ML^2T^{-2} \]

### Summary of dimensions:
- Power: \( [P] = ML^2T^{-3} \)
- Work: \( [W] = ML^2T^{-2} \)
- Torque: \( [τ] = ML^2T^{-2} \)
- Energy: \( [E] = ML^2T^{-2} \)

### Conclusion:
From the analysis, we can see that:
- Power has dimensions \( ML^2T^{-3} \)
- Work, Torque, and Energy all have dimensions \( ML^2T^{-2} \)

Thus, the option that has different dimensions from the remaining three is:
**A. Power**