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. `1.75 xx 10^(5) N`
B. `3.5 xx 10^(5) N`
C. `7.0 xx 10^(5)N`
D. `1. 40 xx 10^(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, \( a = 10 \, \text{m/s}^2 \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \) (assuming standard value for simplicity)

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 Net Force Required for Acceleration:**
- According to Newton's second law, the net force \( F \) required for the upward acceleration is given by:
\[ F = m \cdot a \]
- Substituting the values:
\[ F = 3.5 \times 10^4 \, \text{kg} \times 10 \, \text{m/s}^2 = 3.5 \times 10^5 \, \text{N} \]

4. **Calculate the Total Thrust:**
- The total thrust \( T \) must overcome both the weight of the rocket and provide the force for the upward acceleration:
\[ T = W + F \]
- Since both \( W \) and \( F \) are equal in this case:
\[ T = 3.5 \times 10^5 \, \text{N} + 3.5 \times 10^5 \, \text{N} = 7 \times 10^5 \, \text{N} \]

5. **Final Answer:**
- The initial thrust of the rocket is:
\[ T = 7 \times 10^5 \, \text{N} \]