6. A thin wire was wound le times closely over a bailing tube
The total length of the wire wound
around was found to be
440mm. Calculate the radius of the boiling tube in SI units.



Answer :

To calculate the radius of the boiling tube in SI units when a wire is wound around it, we need to use the formula for the circumference of a circle. The circumference (C) of a circle is given by:

C = 2 π radius

When the wire is wound around the boiling tube 'le' times, the total length of the wire (L) is given by:

L = le C

In this question, we know the total length of the wire L is 440 mm. To convert this length into SI units (meters), we recall that 1 mm equals 0.001 meters. Therefore,

L = 440 mm = 440
0.001 m = 0.440 m

Now let's rearrange the formula for L to solve for the radius of the boiling tube.

Given that:

L = le C

And substituting the circumference C with 2
π radius, we have:

L = le
(2 π radius)

Therefore, to isolate the radius, we divide both sides of the equation by (le 2 π):

radius = L / (le 2 π)

Let's assume 'le' is known. Plug the value of 'le' and the total length L into this formula to find the radius.

For example, if 'le' equals 10, the calculation would be:

radius = 0.440 m / (10 2 π)

radius = 0.440 m / (20 * π)

radius ≈ 0.440 m / 62.83185307

radius ≈ 0.00700637834 m

radius ≈ 7.006 mm

This result gives us the radius of the boiling tube in meters. Remember that the exact value of 'le' would be needed to compute the exact radius; here we assumed 'le' was 10 only as an example. If 'le' were different, we would plug that value into the formula to get the correct radius.