If minutes is the unit of time. `10ms^(-2)` is the unit of acceleration and `100 kg` is the unit of mass, the new unit of work in joule is

Options

A. `10^(5)`
B. `10^(6)`
C. `6xx10^(6)`
D. `36xx10^(6)`

Explanation

To solve the problem step by step, we will first identify the formula for work and then substitute the given values to find the new unit of work in joules.

### Step-by-Step Solution:

1. **Understand the Formula for Work**:
The formula for work (W) is given by:
\[ W = m \cdot a \cdot t^2 \]
where \( m \) is mass, \( a \) is acceleration, and \( t \) is time.

2. **Identify the Given Values**:
- Mass \( m = 100 \, \text{kg} \)
- Acceleration \( a = 10 \, \text{m/s}^2 \)
- Time is given in minutes, which we need to convert to seconds.

3. **Convert Time from Minutes to Seconds**:
Since 1 minute = 60 seconds, we can write:
\[ t = 1 \, \text{minute} = 60 \, \text{seconds} \]

4. **Substitute the Values into the Work Formula**:
Now we substitute the values into the work formula:
\[ W = 100 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot (60 \, \text{s})^2 \]

5. **Calculate \( (60 \, \text{s})^2 \)**:
\[ (60 \, \text{s})^2 = 3600 \, \text{s}^2 \]

6. **Now Substitute Back into the Work Formula**:
\[ W = 100 \, \text{kg} \cdot 10 \, \text{m/s}^2 \cdot 3600 \, \text{s}^2 \]

7. **Calculate the Work**:
\[ W = 100 \cdot 10 \cdot 3600 = 3600000 \, \text{kg m}^2/\text{s}^2 \]
Since \( 1 \, \text{kg m}^2/\text{s}^2 = 1 \, \text{J} \), we have:
\[ W = 3600000 \, \text{J} = 3.6 \times 10^6 \, \text{J} \]

8. **Final Answer**:
The new unit of work in joules is:
\[ W = 3.6 \times 10^6 \, \text{J} \]