A wheel completes 2000 rotations in covering a distance of 9.5 km . The diameter of the wheel is

The correct option is 1.5 m.

Step-by-step Explanation:

To find the diameter of the wheel, we can use the relationship between the total distance traveled by the wheel, the number of rotations, and the circumference of the wheel.

When a wheel completes one full rotation, the distance it covers is equal to its circumference. Therefore, the formula for the total distance covered is:
$\mathrm{Total\; Distance}=\text{Number of rotations}\times \text{Circumference of the wheel}$

Since the circumference of a circle is given by $\pi \times d$ (where $d$ is the diameter), the formula becomes:
$\mathrm{Total\; Distance}=n\times \pi \times d$
where:
- $n$ is the number of rotations = 2000
- $d$ is the diameter of the wheel in meters

Step 1: Convert the distance into meters
The given distance is 9.5 km. Let us convert it into meters:
$\mathrm{Total\; Distance}=9.5\text{km}=9.5\times 1000\text{m}=9500\text{m}$

Step 2: Solve for the diameter (d)
Substitute the values into the formula:
$9500=2000\times \pi \times d$

Now, rearrange the equation to solve for $d$:
$d=\frac{9500}{2000\times \pi }$

Simplify the fraction:
$d=\frac{9.5}{2\times \pi }$

Using the approximation $\pi \approx 3.1416$:
$d=\frac{9.5}{2\times 3.1416}$

$d=\frac{9.5}{6.2832}\approx 1.512\text{m}$

Rounding to the options provided, the diameter of the wheel is approximately 1.5 m.