If the unit of force is 2N, that of length is 4m and that of velocity is `6ms^(-1)`, the unit of mass is

Options

A. `2/9 Kg`
B. `4/3 kg`
C. `9/2 kg `
D. `2/5 kg`

Answer

To find the unit of mass given the units of force, length, and velocity, we can use the relationship defined by Newton's second law of motion, which states that:

\[ F = m \cdot a \]

Where:
- \( F \) is the force,
- \( m \) is the mass,
- \( a \) is the acceleration.

### Step-by-Step Solution:

1. **Understand the given units**:
- Unit of force \( F = 2N \)
- Unit of length \( L = 4m \)
- Unit of velocity \( V = 6ms^{-1} \)

2. **Determine the unit of acceleration**:
- Acceleration \( a \) can be expressed as the change in velocity over time. Since velocity is given as \( 6ms^{-1} \), we can express acceleration as:
\[ a = \frac{V}{t} \]
- We need to find the unit of time \( t \). From the unit of velocity:
\[ V = \frac{L}{t} \implies t = \frac{L}{V} \]
- Substituting the given values:
\[ t = \frac{4m}{6ms^{-1}} = \frac{4}{6}s = \frac{2}{3}s \]

3. **Calculate the unit of acceleration**:
- Now, substituting \( t \) back into the formula for acceleration:
\[ a = \frac{6ms^{-1}}{\frac{2}{3}s} = 6ms^{-1} \cdot \frac{3}{2} = 9ms^{-2} \]

4. **Use the formula for force to find mass**:
- Now, we can use the formula \( F = m \cdot a \):
\[ 2N = m \cdot 9ms^{-2} \]
- Rearranging this gives:
\[ m = \frac{2N}{9ms^{-2}} \]

5. **Convert Newton to mass units**:
- Recall that \( 1N = 1kg \cdot ms^{-2} \):
\[ m = \frac{2(1kg \cdot ms^{-2})}{9ms^{-2}} = \frac{2}{9}kg \]

### Conclusion:
The unit of mass is \( \frac{2}{9} kg \).