A rocket with a lift-off mass `3.5xx10^4 kg` is blasted upwards with an initial acceleration of `10m//s^2`. Then the initial thrust of the blast is

Options

A. `1.75xx10^(5) N`
B. `3.5xx10^(5)N`
C. `7xx10^(5) N`
D. `14xx10^(5) N`

Explanation

To find the initial thrust of the rocket, we can use Newton's second law of motion. The thrust must overcome both the weight of the rocket and provide the necessary force for the upward acceleration.

### Step-by-Step Solution:

1. **Identify the given values**:
- Mass of the rocket, \( m = 3.5 \times 10^4 \, \text{kg} \)
- Acceleration of the rocket, \( a = 10 \, \text{m/s}^2 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

2. **Calculate the weight of the rocket**:
The weight \( W \) of the rocket can be calculated using the formula:
\[ W = m \cdot g \]
Substituting the values:
\[ W = 3.5 \times 10^4 \, \text{kg} \times 10 \, \text{m/s}^2 = 3.5 \times 10^5 \, \text{N} \]

3. **Calculate the total force required for the upward motion**:
The total force \( F \) required to lift the rocket can be calculated using the formula:
\[ F = W + m \cdot a \]
Here, \( m \cdot a \) is the force required to provide the upward acceleration. Thus:
\[ F = W + m \cdot a = 3.5 \times 10^5 \, \text{N} + (3.5 \times 10^4 \, \text{kg} \times 10 \, \text{m/s}^2) \]
\[ = 3.5 \times 10^5 \, \text{N} + 3.5 \times 10^5 \, \text{N} = 7.0 \times 10^5 \, \text{N} \]

4. **Conclusion**:
The initial thrust of the rocket is:
\[ \text{Thrust} = 7.0 \times 10^5 \, \text{N} \]

### Final Answer:
The initial thrust of the blast is \( 7.0 \times 10^5 \, \text{N} \).

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