A balloon os mass 2 KG is rising up with an acceleration of `4m/s^2` . The upward force acting on the balloon is `(g = 10 ms^-2)

Options

A. 0.8 kgf
B. 2.8 kgf
C. 2.4 kgf
D. 2.0 kgf

Answer

To solve the problem, we need to find the upward force acting on the balloon. We can 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.

### Step-by-step Solution:

1. **Identify the given values:**
- Mass of the balloon (m) = 2 kg
- Acceleration of the balloon (a) = 4 m/s²
- Acceleration due to gravity (g) = 10 m/s²

2. **Calculate the weight of the balloon:**
The weight (W) of the balloon acts downward and is given by the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 2 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 20 \, \text{N} \]

3. **Apply Newton’s second law:**
According to Newton's second law, the net force (F_net) acting on the balloon can be expressed as:
\[ F_{\text{up}} - W = m \cdot a \]
where \( F_{\text{up}} \) is the upward force acting on the balloon. Rearranging the equation gives:
\[ F_{\text{up}} = W + m \cdot a \]

4. **Substitute the known values into the equation:**
Now, substituting the values we have:
\[ F_{\text{up}} = 20 \, \text{N} + (2 \, \text{kg} \cdot 4 \, \text{m/s}^2) \]
\[ F_{\text{up}} = 20 \, \text{N} + 8 \, \text{N} = 28 \, \text{N} \]

5. **Convert the force to kg-force:**
To express the force in kg-force, we divide by the acceleration due to gravity (g):
\[ F_{\text{up}} = \frac{28 \, \text{N}}{10 \, \text{m/s}^2} = 2.8 \, \text{kg-force} \]

### Final Answer:
The upward force acting on the balloon is **2.8 kg-force**.

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