250 N force is required to raise 75 kg mass from a pulley. If rope is pulled 12 m then the load is lifted to 3m, the efficiency of pulley system will be : -

Options

A. `25%`
B. `33.3%`
C. `75%`
D. `90%`

Explanation

To find the efficiency of the pulley system, we will follow these steps:

### Step 1: Identify the useful work done
The useful work done (W_useful) is the work done to lift the mass. This can be calculated using the formula:
\[ W_{\text{useful}} = mgh \]
where:
- \( m = 75 \, \text{kg} \) (mass)
- \( g = 10 \, \text{m/s}^2 \) (acceleration due to gravity)
- \( h = 3 \, \text{m} \) (height lifted)

### Step 2: Calculate the useful work done
Substituting the values into the formula:
\[ W_{\text{useful}} = 75 \, \text{kg} \times 10 \, \text{m/s}^2 \times 3 \, \text{m} \]
\[ W_{\text{useful}} = 75 \times 10 \times 3 = 2250 \, \text{J} \]

### Step 3: Identify the total work done
The total work done (W_total) is the work done by the applied force. This can be calculated using the formula:
\[ W_{\text{total}} = F \times d \]
where:
- \( F = 250 \, \text{N} \) (force applied)
- \( d = 12 \, \text{m} \) (distance the rope is pulled)

### Step 4: Calculate the total work done
Substituting the values into the formula:
\[ W_{\text{total}} = 250 \, \text{N} \times 12 \, \text{m} \]
\[ W_{\text{total}} = 3000 \, \text{J} \]

### Step 5: Calculate the efficiency
Efficiency (η) is given by the ratio of useful work done to total work done:
\[ \eta = \frac{W_{\text{useful}}}{W_{\text{total}}} \]
Substituting the values:
\[ \eta = \frac{2250 \, \text{J}}{3000 \, \text{J}} \]
\[ \eta = 0.75 \]

### Step 6: Convert efficiency to percentage
To express efficiency as a percentage, multiply by 100:
\[ \eta_{\text{percentage}} = 0.75 \times 100 = 75\% \]

### Final Answer
The efficiency of the pulley system is **75%**.

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