In a particular system the units of length, mass and time are chosen to be `10 cm, 10 g` and `0.1 s` respectively. The unit of force in this system will be equal to

Options

A. `0.1N`
B. `1N`
C. `10N`
D. `100N`

Explanation

To find the unit of force in the given system where the units of length, mass, and time are defined as \(10 \, \text{cm}\), \(10 \, \text{g}\), and \(0.1 \, \text{s}\) respectively, we will follow these steps:

### Step-by-Step Solution:

1. **Identify the SI Units for Force**:
The SI unit of force is the Newton (N), which can be expressed in terms of base units as:
\[ 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \]
This can be represented dimensionally as:
\[ [F] = [M][L][T]^{-2} \]

2. **Convert the Given Units to SI Units**:
- **Length**: The given length is \(10 \, \text{cm}\). To convert to meters:
\[ 10 \, \text{cm} = \frac{10}{100} \, \text{m} = 0.1 \, \text{m} \]
- **Mass**: The given mass is \(10 \, \text{g}\). To convert to kilograms:
\[ 10 \, \text{g} = \frac{10}{1000} \, \text{kg} = 0.01 \, \text{kg} \]
- **Time**: The given time is \(0.1 \, \text{s}\), which is already in SI units.

3. **Substitute the Converted Values into the Force Formula**:
Now we can substitute the converted values into the formula for force:
\[ F = m \cdot \frac{l}{t^2} \]
where \(m = 0.01 \, \text{kg}\), \(l = 0.1 \, \text{m}\), and \(t = 0.1 \, \text{s}\).
\[ F = 0.01 \cdot \frac{0.1}{(0.1)^2} \]

4. **Calculate the Force**:
First, calculate \((0.1)^2\):
\[ (0.1)^2 = 0.01 \]
Now substitute this back into the equation:
\[ F = 0.01 \cdot \frac{0.1}{0.01} \]
Simplifying gives:
\[ F = 0.01 \cdot 10 = 0.1 \, \text{N} \]

5. **Final Answer**:
Therefore, the unit of force in this system is:
\[ \boxed{0.1 \, \text{N}} \]