The mechanical advantage of a wheel axle is 5 what will be thereforce required to lift a 200kg wt?

Options

A. 10kg wt.
B. 2 kg wt.
C. 20 kg wt.
D. 40 kg wt.

Explanation

To solve the problem, we need to find the effort required to lift a weight of 200 kg using a wheel and axle system with a mechanical advantage (MA) of 5.

### Step-by-Step Solution:

1. **Understand the Concept of Mechanical Advantage (MA)**:
The mechanical advantage of a machine is defined as the ratio of the load (weight being lifted) to the effort (force applied). It can be expressed mathematically as:
\[ \text{MA} = \frac{\text{Load}}{\text{Effort}} \]

2. **Identify the Given Values**:
- Load (weight to be lifted) = 200 kg
- Mechanical Advantage (MA) = 5

3. **Convert Load to Newtons**:
Since weight is a force, we need to convert the mass (in kg) to weight (in Newtons) using the formula:
\[ \text{Weight} = \text{mass} \times g \]
where \( g \) (acceleration due to gravity) is approximately \( 9.81 \, \text{m/s}^2 \).
\[ \text{Weight} = 200 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 1962 \, \text{N} \]

4. **Use the Mechanical Advantage Formula to Find Effort**:
Rearranging the formula for mechanical advantage to find the effort:
\[ \text{Effort} = \frac{\text{Load}}{\text{MA}} \]
Substituting the values we have:
\[ \text{Effort} = \frac{1962 \, \text{N}}{5} = 392.4 \, \text{N} \]

5. **Convert Effort Back to kg**:
To express the effort in kilograms, we can use the relationship:
\[ \text{Effort (kg)} = \frac{\text{Effort (N)}}{g} \]
\[ \text{Effort (kg)} = \frac{392.4 \, \text{N}}{9.81 \, \text{m/s}^2} \approx 40 \, \text{kg} \]

6. **Conclusion**:
The effort required to lift a 200 kg weight using a wheel and axle with a mechanical advantage of 5 is approximately 40 kg.

### Final Answer:
The effort required is **40 kg**.