A particle of mass 2 kg is projected vertically upward with a velocity of 20 m/s. It attains maximum height of 17 m. The loss in mechanical energy due to air drag is `( g = 10 ms^-2)`

Options

A. 100 J
B. 60 J
C. 80 J
D. Zero

Answer

To solve the problem, we need to find the loss in mechanical energy due to air drag when a particle of mass 2 kg is projected vertically upward with an initial velocity of 20 m/s and reaches a maximum height of 17 m.

### Step-by-Step Solution:

1. **Calculate Initial Kinetic Energy (KE_initial)**:
The initial kinetic energy of the particle can be calculated using the formula:
\[ KE_{\text{initial}} = \frac{1}{2} m v^2 \]
where \( m = 2 \, \text{kg} \) and \( v = 20 \, \text{m/s} \).
\[ KE_{\text{initial}} = \frac{1}{2} \times 2 \times (20)^2 = 1 \times 400 = 400 \, \text{J} \]

2. **Calculate Potential Energy at Maximum Height (PE_max)**:
The potential energy at the maximum height can be calculated using the formula:
\[ PE_{\text{max}} = mgh \]
where \( g = 10 \, \text{m/s}^2 \) and \( h = 17 \, \text{m} \).
\[ PE_{\text{max}} = 2 \times 10 \times 17 = 340 \, \text{J} \]

3. **Apply Conservation of Energy Principle**:
According to the conservation of energy, the loss in mechanical energy due to air drag can be calculated as:
\[ \text{Loss in Mechanical Energy} = KE_{\text{initial}} - PE_{\text{max}} \]
Substituting the values we calculated:
\[ \text{Loss in Mechanical Energy} = 400 \, \text{J} - 340 \, \text{J} = 60 \, \text{J} \]

4. **Conclusion**:
Therefore, the loss in mechanical energy due to air drag is \( 60 \, \text{J} \).

### Final Answer:
The loss in mechanical energy due to air drag is **60 Joules**.

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