Imagine a system of units in which the unit of mass is 100 kg, length is 1 km and time is 1 minute Then 1 joule in this system is equal to

Options

A. 360
B. 3.6
C. `36xx10^5`
D. `36xx10^(-6)`

Answer

To solve the problem, we need to convert the standard unit of energy (joule) into the new system of units defined in the question. Let's break it down step by step.

### Step 1: Understand the Units
In the new system of units:
- The unit of mass is 100 kg.
- The unit of length is 1 km (which is equal to \(1 \times 10^3\) m).
- The unit of time is 1 minute (which is equal to 60 seconds).

### Step 2: Recall the Definition of Joule
The joule (J) is defined as:
\[ 1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2 \]
This means that 1 joule is equivalent to 1 kilogram meter squared per second squared.

### Step 3: Substitute the New Units into the Joule Definition
In the new system:
- Mass (kg) = 100 kg
- Length (m) = \(1 \times 10^3\) m
- Time (s) = 60 s

Now, substituting these values into the definition of joule:
\[ 1 \text{ J}' = (100 \text{ kg}) \cdot (1 \times 10^3 \text{ m})^2 / (60 \text{ s})^2 \]

### Step 4: Calculate the New Joule Value
Now, we can calculate:
\[ 1 \text{ J}' = 100 \cdot (1 \times 10^3)^2 / (60^2) \]
Calculating each part:
- \((1 \times 10^3)^2 = 1 \times 10^6\)
- \(60^2 = 3600\)

So, we have:
\[ 1 \text{ J}' = 100 \cdot \frac{1 \times 10^6}{3600} \]

### Step 5: Simplify the Expression
Now, simplify the expression:
\[ 1 \text{ J}' = \frac{100 \times 10^6}{3600} \]
Calculating \(100/3600\):
\[ \frac{100}{3600} = \frac{1}{36} \]
Thus:
\[ 1 \text{ J}' = \frac{10^6}{36} \]

### Step 6: Final Conversion
To express this in terms of joules:
\[ 1 \text{ J} = \frac{10^6}{36} \text{ J}' = 36 \times 10^{-6} \text{ J}' \]

### Conclusion
Thus, in the new system of units, 1 joule is equal to:
\[ \boxed{36 \times 10^{-6} \text{ J}'} \]