For a system of pulleys, the mechanical advantage is 4. Taking `g = 10m//s^(2)`, the force required to lift a mass of 100 kg by it is

Options

A. 50 N
B. 150 N
C. 200 N
D. 250 N

Answer

To solve the problem step by step, we will use the concept of mechanical advantage (MA) and the formula for weight.

### Step 1: Calculate the weight of the mass
The weight (W) of an object is given by the formula:
\[ W = m \cdot g \]
where:
- \( m \) = mass of the object (in kg)
- \( g \) = acceleration due to gravity (in m/s²)

Given:
- \( m = 100 \, \text{kg} \)
- \( g = 10 \, \text{m/s}^2 \)

Calculating the weight:
\[ W = 100 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 1000 \, \text{N} \]

### Step 2: Use the mechanical advantage formula
The mechanical advantage (MA) is defined as:
\[ MA = \frac{\text{Output Force}}{\text{Input Force}} \]

We know:
- Output Force = Weight of the mass = 1000 N
- Mechanical Advantage = 4

Rearranging the formula to find the Input Force (F_in):
\[ F_{in} = \frac{\text{Output Force}}{MA} \]

### Step 3: Substitute the known values
Substituting the known values into the equation:
\[ F_{in} = \frac{1000 \, \text{N}}{4} \]

### Step 4: Calculate the Input Force
Calculating the input force:
\[ F_{in} = 250 \, \text{N} \]

### Conclusion
The force required to lift a mass of 100 kg using the pulley system is **250 N**.

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