The dimensions of potential energy of an object in mass, length and time are respectively

Options

A. 2,2,1
B. 1,2,-2
C. `-2,1,2`
D. `1,-1,2`

Answer

To find the dimensions of potential energy, we can start with the formula for potential energy:

1. **Identify the formula for potential energy**:
The potential energy (PE) of an object is given by the formula:
\[ PE = mgh \]
where \( m \) is mass, \( g \) is the acceleration due to gravity, and \( h \) is the height.

2. **Identify the units of each variable**:
- Mass (\( m \)) is measured in kilograms (kg).
- The acceleration due to gravity (\( g \)) is measured in meters per second squared (m/s²).
- Height (\( h \)) is measured in meters (m).

3. **Combine the units**:
Substituting the units into the formula for potential energy, we have:
\[ PE = m \cdot g \cdot h = \text{kg} \cdot \left(\frac{\text{m}}{\text{s}^2}\right) \cdot \text{m} \]
Simplifying this gives:
\[ PE = \text{kg} \cdot \text{m}^2 \cdot \text{s}^{-2} \]

4. **Express in terms of dimensions**:
Now, we can express the units in terms of dimensions:
- Mass (m) has a dimension of \( [M] \).
- Length (l) has a dimension of \( [L] \).
- Time (t) has a dimension of \( [T] \).

Therefore, the dimensions of potential energy can be written as:
\[ [PE] = [M^1 L^2 T^{-2}] \]

5. **Final answer**:
The dimensions of potential energy in terms of mass, length, and time are:
\[ [M^1 L^2 T^{-2}] \]