The gravitational unit of what( kg-m) equal to

Options

A. `9.8`Newton
B. `9.8`Joule
C. `10^7`Joule
D. `10^7`Newton

Answer

To solve the question regarding the gravitational unit of work (kg-m), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Work Done Against Gravity**:
The work done against gravity when lifting an object is related to its potential energy. The formula for gravitational potential energy (U) is given by:
\[ U = mgh \]
where:
- \( U \) is the potential energy (or work done),
- \( m \) is the mass of the object (in kg),
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)),
- \( h \) is the height (in meters).

2. **Identifying Units**:
The unit of work (or energy) in the International System of Units (SI) is the joule (J). One joule is defined as the work done when a force of one newton displaces an object by one meter in the direction of the force.

3. **Relating kg-m to Joules**:
We can express the work done against gravity in terms of its units:
\[ \text{Work} = mgh \]
The units of each component are:
- Mass \( m \) in kilograms (kg),
- Height \( h \) in meters (m),
- Acceleration due to gravity \( g \) in meters per second squared (m/s²).

Therefore, the unit of work can be expressed as:
\[ \text{Unit of Work} = \text{kg} \cdot \text{m} \cdot \text{m/s}^2 = \text{kg} \cdot \text{m}^2/\text{s}^2 \]
This is equivalent to 1 joule (J).

4. **Calculating Gravitational Work**:
If we consider a specific case where \( g \) is approximately \( 9.8 \, \text{m/s}^2 \), we can express the gravitational unit of work as:
\[ \text{Gravitational Work} = mgh = m \cdot 9.8 \cdot h \]
For a unit mass (1 kg) and a height of 1 meter, the work done is:
\[ \text{Gravitational Work} = 1 \cdot 9.8 \cdot 1 = 9.8 \, \text{J} \]

5. **Conclusion**:
Thus, the gravitational unit of work (kg-m) is equivalent to approximately 9.8 joules.

### Final Answer:
The gravitational unit of work (kg-m) is equal to approximately 9.8 joules.

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