Given: n = 6, l = 10 m, R = 450 m and V = 72 km/h

The extra widening required in a 6-lane carriage when the length of the vehicle is 10 m, the radius of the curve is 450 m, and the speed is 72 kmph can be calculated using the formula for centrifugal force.

Let's break down the solution into the following steps:

1. Calculate the centrifugal force:
The centrifugal force acting on a vehicle moving in a curved path can be determined using the formula:

F = (m * v^2) / r

Where:
F is the centrifugal force
m is the mass of the vehicle
v is the velocity of the vehicle
r is the radius of the curve

2. Calculate the mass of the vehicle:
Since the length of the vehicle is given as 10 m, we can assume a width of around 2.5 m for a typical car. Therefore, the area of the vehicle can be calculated as:

A = length * width = 10 m * 2.5 m = 25 m^2

Assuming a density of 1.2 kg/m^3 for the vehicle, we can calculate the mass as:

m = density * volume = 1.2 kg/m^3 * 25 m^2 = 30 kg

3. Convert the speed from kmph to m/s:
Given that the speed is 72 kmph, we need to convert it to m/s by dividing it by 3.6:

v = 72 kmph / 3.6 = 20 m/s

4. Convert the radius from meters to centimeters:
Given that the radius is 450 m, we need to convert it to centimeters by multiplying it by 100:

r = 450 m * 100 = 45000 cm

5. Substitute the values into the centrifugal force formula:
Using the calculated values for mass (m), velocity (v), and radius (r), we can now calculate the centrifugal force:

F = (30 kg * (20 m/s)^2) / 45000 cm = 1.333 N

6. Calculate the extra widening required:
To calculate the extra widening required in the 6-lane carriage, we need to consider the centrifugal force acting on the vehicle. The extra widening required can be determined using the formula:

W = F / (N * (h - g))

Where:
W is the extra widening required
F is the centrifugal force
N is the number of lanes
h is the height of the center of gravity of the vehicle
g is the height of the center of gravity of the vehicle's outer edge

Assuming the heights of the center of gravity and the vehicle's outer edge are approximately the same, we can simplify the formula to:

W = F / (N * h)

Given that the number of lanes is 6, we can calculate the extra widening required:

W = 1.333 N / (6 * h)

Since the answer is expected in meters, we divide the result by 100:

W = 1.333 N / (6 * h) / 100 = 0.00222 / h

7. Calculate the extra widening required for a typical vehicle:
Assuming a typical height of the center of gravity for a car is around 1.5 m, we can substitute this value into the formula:

W = 0.00222 / 1.5 =