A balloon of mass 10 kf is raising up with an acceleration of `20 ms^(-2)`. If a mass of 4 kg is removed from the balloon its acceleration becomes ( take, `g=10ms^(-2)`)

Options

A. `40 ms^(-2)`
B. `20 ms^(-2)`
C. `30 ms^(-2)`
D. `12 ms^(-2)`

Explanation

To solve the problem, we need to find the new acceleration of the balloon after removing a mass of 4 kg. We will use Newton's second law of motion, which states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma).

### Step-by-Step Solution:

1. **Identify the initial conditions:**
- Mass of the balloon (m_initial) = 10 kg
- Acceleration (a_initial) = 20 m/s²
- Gravitational acceleration (g) = 10 m/s²

2. **Calculate the initial force acting on the balloon:**
- The net force (F_initial) can be calculated using the formula:
\[ F_{\text{initial}} = m_{\text{initial}} \cdot (g + a_{\text{initial}}) \]
- Substituting the values:
\[ F_{\text{initial}} = 10 \, \text{kg} \cdot (10 \, \text{m/s}^2 + 20 \, \text{m/s}^2) = 10 \, \text{kg} \cdot 30 \, \text{m/s}^2 = 300 \, \text{N} \]

3. **Determine the new mass after removing 4 kg:**
- New mass (m_new) = m_initial - 4 kg = 10 kg - 4 kg = 6 kg

4. **Calculate the weight of the new mass:**
- Weight (W_new) = m_new * g
- Substituting the values:
\[ W_{\text{new}} = 6 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 60 \, \text{N} \]

5. **Calculate the new net force acting on the balloon:**
- The new net force (F_new) can be calculated as:
\[ F_{\text{new}} = F_{\text{initial}} - W_{\text{new}} \]
- Substituting the values:
\[ F_{\text{new}} = 300 \, \text{N} - 60 \, \text{N} = 240 \, \text{N} \]

6. **Calculate the new acceleration of the balloon:**
- Using Newton's second law (F = ma), we can find the new acceleration (a_new):
\[ a_{\text{new}} = \frac{F_{\text{new}}}{m_{\text{new}}} \]
- Substituting the values:
\[ a_{\text{new}} = \frac{240 \, \text{N}}{6 \, \text{kg}} = 40 \, \text{m/s}^2 \]

### Final Answer:
The new acceleration of the balloon after removing the 4 kg mass is **40 m/s²**.