The diamensions of time in energy are

Options

A. 0
B. -2
C. 2
D. 1

Answer

To find the dimensions of time in energy, we will follow these steps:

### Step 1: Understand the relationship between energy and work
Energy is defined as the ability to do work. The most common formula for work (and hence energy) is given by:
\[ \text{Work} = \text{Force} \times \text{Distance} \]

### Step 2: Write the formula for force
Force can be expressed using Newton's second law:
\[ \text{Force} = \text{Mass} \times \text{Acceleration} \]
Acceleration can be defined as the change in velocity over time, which is:
\[ \text{Acceleration} = \frac{\text{Change in velocity}}{\text{Time}} = \frac{\text{Length}}{\text{Time}^2} \]
Thus, the dimension of force can be expressed as:
\[ \text{Force} = \text{Mass} \times \frac{\text{Length}}{\text{Time}^2} \]

### Step 3: Write the dimensions of force
The dimension of mass is represented as \( [M] \), the dimension of length as \( [L] \), and the dimension of time as \( [T] \). Therefore, the dimension of force is:
\[ [F] = [M] \times \left[\frac{L}{T^2}\right] = [M L T^{-2}] \]

### Step 4: Substitute the dimensions of force into the work formula
Now, substituting the dimensions of force into the work formula gives:
\[ [\text{Work}] = [F] \times [L] = [M L T^{-2}] \times [L] = [M L^2 T^{-2}] \]

### Step 5: Conclusion about the dimensions of energy
Since work and energy are equivalent, we can conclude that the dimensions of energy are:
\[ [E] = [M L^2 T^{-2}] \]

### Step 6: Identify the power of time in the dimensions of energy
From the dimensions of energy, we can see that the power of time \( T \) is \( -2 \). Therefore, the dimensions of time in energy are:
\[ T^{-2} \]

### Final Answer
The dimensions of time in energy are \( T^{-2} \).

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