An aeroplane requires a speed of 72 kmph for a take off with 150m run on the ground. The mass of the plane is 1500kg and the coefficient of friction between the aeroplane and the ground is 0.4. Assuming that the aeroplane acceleration uniformly during take off, find the minimum force exerted by the engine of the aeroplane for take off. 

Options

A. 8500 N
B. 7880 N
C. 9000 N
D. 6500 N

Answer

To solve the problem, we will follow these steps:

### Step 1: Convert the speed from km/h to m/s
The speed required for takeoff is given as 72 km/h. We need to convert this to meters per second (m/s).

\[ \text{Speed in m/s} = \frac{72 \text{ km/h} \times 1000 \text{ m/km}}{3600 \text{ s/h}} = 20 \text{ m/s} \]

### Step 2: Use the kinematic equation to find acceleration
We know the initial speed \( u = 0 \), final speed \( v = 20 \text{ m/s} \), and the distance \( s = 150 \text{ m} \). We can use the kinematic equation:

\[ v^2 = u^2 + 2as \]

Substituting the known values:

\[ (20)^2 = 0 + 2a(150) \]

\[ 400 = 300a \]

Solving for \( a \):

\[ a = \frac{400}{300} = \frac{4}{3} \text{ m/s}^2 \]

### Step 3: Calculate the frictional force
The frictional force \( f_{\text{friction}} \) can be calculated using the formula:

\[ f_{\text{friction}} = \mu \cdot N \]

Where \( N \) is the normal force, which is equal to the weight of the airplane:

\[ N = mg \]

Given:
- Mass \( m = 1500 \text{ kg} \)
- Coefficient of friction \( \mu = 0.4 \)
- Acceleration due to gravity \( g = 9.8 \text{ m/s}^2 \)

Calculating \( N \):

\[ N = 1500 \cdot 9.8 = 14700 \text{ N} \]

Now calculating the frictional force:

\[ f_{\text{friction}} = 0.4 \cdot 14700 = 5880 \text{ N} \]

### Step 4: Calculate the minimum force exerted by the engine
Using Newton's second law, the net force \( F \) acting on the airplane is given by:

\[ F = ma + f_{\text{friction}} \]

Substituting the values we have:

\[ F = 1500 \cdot \frac{4}{3} + 5880 \]

Calculating \( F \):

\[ F = 2000 + 5880 = 7880 \text{ N} \]

### Conclusion
The minimum force exerted by the engine of the aeroplane for takeoff is:

\[ \boxed{7880 \text{ N}} \]