1 joule of energy is to be converted into new system of units in which length is measured in 10 metre, mass in 10 kg and time in 1 minute. The numerical value of 1 J in the new system is :-

Options

A. `36xx10^(-4)`
B. `36xx10^(-3)`
C. `36xx10^(-2)`
D. `36xx10^(-1)`

Answer

To convert 1 joule of energy into a new system of units where length is measured in 10 meters, mass in 10 kg, and time in 1 minute, we can follow these steps:

### Step 1: Understand the definition of Joule
1 Joule (J) is defined as the amount of energy transferred when a force of 1 newton is applied over a distance of 1 meter. In terms of base units, 1 joule can be expressed as:
\[ 1 \text{ J} = 1 \text{ kg} \cdot \text{m}^2/\text{s}^2 \]

### Step 2: Define the new units
In the new system:
- Length = 10 meters
- Mass = 10 kg
- Time = 1 minute = 60 seconds

### Step 3: Substitute the new units into the formula for Joules
Using the new units, we can express the joule in the new system:
\[ \text{J} = \text{mass} \times \text{length}^2 / \text{time}^2 \]
Substituting the new units:
\[ \text{J}' = (10 \text{ kg}) \times (10 \text{ m})^2 / (1 \text{ min})^2 \]
\[ = (10 \text{ kg}) \times (10^2 \text{ m}^2) / (60 \text{ s})^2 \]
\[ = 10 \times 100 \text{ kg} \cdot \text{m}^2 / 3600 \text{ s}^2 \]
\[ = 1000 \text{ kg} \cdot \text{m}^2 / 3600 \text{ s}^2 \]

### Step 4: Simplify the expression
Now, we simplify:
\[ = \frac{1000}{3600} \text{ J} \]
\[ = \frac{10}{36} \text{ J} \]

### Step 5: Convert to scientific notation
To express this in scientific notation:
\[ \frac{10}{36} = \frac{1}{3.6} \approx 0.2777 \text{ J} \]
In scientific notation, this is approximately:
\[ = 36 \times 10^{-2} \text{ J} \]

### Conclusion
Thus, the numerical value of 1 joule in the new system of units is:
\[ \text{Answer} = 36 \times 10^{-2} \]

### Final Answer
The correct option is: **36 x 10 to the power -2**.

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