A man of mass 60kg lifts a 15 kg mass to the top of a building of height 10 m in 5 minutes. H is efficiency is

Options

A. 0.1
B. 0.2
C. 0.3
D. 0.4

Answer

To find the efficiency of the man lifting a mass, we can follow these steps:

### Step 1: Calculate the total work done by the man
The total work done (W_total) is equal to the force exerted by the man multiplied by the distance he lifts the weight. The force exerted includes both his weight and the weight of the mass he is lifting.

1. **Calculate the total mass**:
\[ \text{Total mass} = \text{mass of man} + \text{mass lifted} = 60 \, \text{kg} + 15 \, \text{kg} = 75 \, \text{kg} \]

2. **Calculate the weight (force)**:
\[ \text{Weight} = \text{Total mass} \times g = 75 \, \text{kg} \times 10 \, \text{m/s}^2 = 750 \, \text{N} \]

3. **Calculate the work done**:
\[ W_{\text{total}} = \text{Weight} \times \text{height} = 750 \, \text{N} \times 10 \, \text{m} = 7500 \, \text{J} \]

### Step 2: Calculate the useful work done on the mass
The useful work done (W_useful) is the work done specifically on the mass being lifted.

1. **Calculate the work done on the mass**:
\[ W_{\text{useful}} = \text{mass lifted} \times g \times \text{height} = 15 \, \text{kg} \times 10 \, \text{m/s}^2 \times 10 \, \text{m} = 1500 \, \text{J} \]

### Step 3: Calculate the efficiency
Efficiency (η) is calculated as the ratio of useful work done to the total work done.

1. **Calculate efficiency**:
\[ \eta = \frac{W_{\text{useful}}}{W_{\text{total}}} = \frac{1500 \, \text{J}}{7500 \, \text{J}} = 0.2 \]

### Final Result
The efficiency of the man is 0.2 or 20%.

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