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. (a) `3.5xx10^5N`
B. (b) `7.0xx10^5N`
C. (c) `14.0xx10^5N`
D. (d) `1.75xx10^5N`

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. Here’s how we can solve the problem step by step:

### Step 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, \( g = 10 \, \text{m/s}^2 \) (approximately)

### Step 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:
\[ W = 3.5 \times 10^4 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 3.5 \times 10^5 \, \text{N} \]

### Step 3: Apply Newton's second law
According to Newton's second law, the net force \( F_{\text{net}} \) acting on the rocket is given by:
\[ F_{\text{net}} = m \cdot a \]
Substituting the values:
\[ F_{\text{net}} = 3.5 \times 10^4 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 3.5 \times 10^5 \, \text{N} \]

### Step 4: Calculate the total thrust
The total thrust \( F \) must overcome both the weight of the rocket and provide the upward acceleration. Therefore, we can express the thrust as:
\[ F = W + F_{\text{net}} \]
Substituting the values we calculated:
\[ F = 3.5 \times 10^5 \, \text{N} + 3.5 \times 10^5 \, \text{N} = 7.0 \times 10^5 \, \text{N} \]

### Final Answer
The initial thrust of the rocket is:
\[ F = 7.0 \times 10^5 \, \text{N} \]