A force of 40N acts on a body. If the units of mass and length are doubled and the unit of time is tripled, then the force in the new system becomes 

Options

A. 90 N
B. 90 new units
C. `160/9 ` new units
D. `160/9` N

Answer

To solve the problem, we need to understand how the changes in the units of mass, length, and time affect the force. We start with the known relationship of force in the SI system and then apply the changes to find the new force in the modified unit system.

### Step-by-Step Solution:

1. **Understand the given force**:
The force acting on the body is given as \( F = 40 \, \text{N} \).

2. **Recall the definition of force**:
In SI units, force is defined as:
\[ 1 \, \text{N} = 1 \, \text{kg} \cdot \text{m/s}^2 \]
Therefore, we can express force in terms of mass (m), length (l), and time (t):
\[ F = m \cdot l \cdot t^{-2} \]

3. **Identify the changes in units**:
- The units of mass are doubled: \( m' = 2m \)
- The units of length are doubled: \( l' = 2l \)
- The units of time are tripled: \( t' = 3t \)

4. **Substitute the new units into the force equation**:
The new force \( F' \) can be expressed as:
\[ F' = m' \cdot l' \cdot (t')^{-2} \]
Substituting the modified units:
\[ F' = (2m) \cdot (2l) \cdot (3t)^{-2} \]

5. **Simplify the expression**:
\[ F' = 2m \cdot 2l \cdot \frac{1}{(3^2 \cdot t^2)} = \frac{4ml}{9t^2} \]

6. **Relate the new force to the original force**:
Since \( F = ml/t^2 \), we can express \( F' \) in terms of \( F \):
\[ F' = \frac{4}{9} \cdot F \]

7. **Substitute the original force value**:
\[ F' = \frac{4}{9} \cdot 40 \, \text{N} = \frac{160}{9} \, \text{N} \]

8. **Final answer**:
Thus, the force in the new system becomes:
\[ F' = \frac{160}{9} \, \text{N} \]