In a new system of units, unit of mass is 10 kg, unit of length is 100 m, unit of time is 1 minutes. The magnitude of 1 N force in new system of units will be

Options

A. 36
B. 60
C. 3.6
D. 0.06

Explanation

To find the magnitude of 1 N force in the new system of units, we need to convert the units of mass, length, and time into the new system and then calculate the force using the formula for force.

### Step-by-Step Solution:

1. **Understand the definition of force**:
The force \( F \) is defined as \( F = m \cdot a \), where \( m \) is mass and \( a \) is acceleration.

2. **Identify the units in the new system**:
- Unit of mass = 10 kg
- Unit of length = 100 m
- Unit of time = 1 minute = 60 seconds

3. **Convert 1 N to the new units**:
We know that 1 N (Newton) is equivalent to \( 1 \, \text{kg} \cdot \text{m/s}^2 \).

4. **Convert mass**:
In the new system, 1 kg is represented as \( \frac{1}{10} \) of the new unit of mass. Therefore, we have:
\[ m = 1 \, \text{kg} = \frac{1}{10} \, \text{(new unit of mass)} \]

5. **Convert acceleration**:
Acceleration is given in meters per second squared. We need to convert the units of length and time:
- For length: \( 1 \, \text{m} = \frac{1}{100} \, \text{(new unit of length)} \)
- For time: \( 1 \, \text{s} = \frac{1}{60} \, \text{(new unit of time)} \)

Therefore, acceleration in the new units can be calculated as:
\[ a = \frac{1 \, \text{m}}{(1 \, \text{s})^2} = \frac{1/100 \, \text{(new unit of length)}}{(1/60 \, \text{(new unit of time)})^2} \]
Simplifying this gives:
\[ a = \frac{1/100}{(1/60)^2} = \frac{1/100}{1/3600} = \frac{3600}{100} = 36 \, \text{(new unit of acceleration)} \]

6. **Calculate the force in new units**:
Now substituting the values of mass and acceleration into the force equation:
\[ F = m \cdot a = \left(\frac{1}{10}\right) \cdot 36 = \frac{36}{10} = 3.6 \, \text{(new unit of force)} \]

### Final Answer:
The magnitude of 1 N force in the new system of units will be **3.6**.