A rocket is going upwards with accelerated motion A man sitting in the rocket feels his weight becomes 5 times If mass of rocket inculding that of the man is `0.1 xx 10^(4)kg` how much force is beigh applied by rocket engine? Take `g = 10m//s^(2)` .

Explanation

To solve the problem, we need to find the force being applied by the rocket engine when a man inside the rocket feels that his weight has increased to 5 times its normal weight due to the rocket's acceleration.

### Step-by-Step Solution:

1. **Understanding the Concept of Weight**:
The weight of an object is given by the formula:
\[ W = m \cdot g \]
where \( W \) is the weight, \( m \) is the mass of the object, and \( g \) is the acceleration due to gravity.

2. **Normal Weight Calculation**:
The normal weight of the man (or the total weight of the rocket including the man) can be calculated using the given mass:
\[ m = 0.1 \times 10^4 \, \text{kg} = 1000 \, \text{kg} \]
The weight at normal conditions (without any acceleration) is:
\[ W_0 = m \cdot g = 1000 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 10000 \, \text{N} \]

3. **Weight Under Acceleration**:
When the man feels his weight is 5 times, the effective weight \( W \) becomes:
\[ W = 5 \cdot W_0 = 5 \cdot 10000 \, \text{N} = 50000 \, \text{N} \]

4. **Finding the Net Force**:
The net force \( F \) acting on the rocket (which is also the force exerted by the rocket engine) can be calculated using Newton's second law:
\[ F = m \cdot a \]
Here, \( a \) is the effective acceleration experienced by the man, which can be derived from the effective weight:
\[ W = m \cdot (g + a) \]
Rearranging gives:
\[ 50000 \, \text{N} = 1000 \, \text{kg} \cdot (10 \, \text{m/s}^2 + a) \]
Simplifying this:
\[ 50000 = 10000 + 1000a \]
\[ 50000 - 10000 = 1000a \]
\[ 40000 = 1000a \]
\[ a = \frac{40000}{1000} = 40 \, \text{m/s}^2 \]

5. **Calculating the Total Force**:
Now, substituting \( a \) back into the equation for force:
\[ F = m \cdot (g + a) = 1000 \, \text{kg} \cdot (10 \, \text{m/s}^2 + 40 \, \text{m/s}^2) \]
\[ F = 1000 \, \text{kg} \cdot 50 \, \text{m/s}^2 = 50000 \, \text{N} \]

### Final Answer:
The force being applied by the rocket engine is:
\[ F = 50000 \, \text{N} \]