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.
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.
