Question

The diameter of the kernel of a circular section of diameter \(d\) is

• A. \(\dfrac{d}{2}\)
• B. \(\dfrac{d}{3}\)
• C. \(\dfrac{d}{4}\)
• D. \(\dfrac{d}{\sqrt{2}}\)

Hint:

Kernel dimensions: \[ \boxed{ \begin{aligned} \text{Rectangle: }&\frac{b}{6}\times\frac{d}{6}\\ \text{Circle: }&\text{Kernel diameter}=\frac{d}{4} \end{aligned} } \]

Answer 1

The Correct Option is C

Step 1: Recall the general formula for the kernel distance.
The kernel (or core) distance of any section is given by the ratio of its section modulus to its area: \[ k = \frac{Z}{A}. \]
Step 2: Work this out for a circular section of diameter $d$.
\[ Z = \frac{\pi d^3}{32}, \qquad A = \frac{\pi d^2}{4}. \] So \[ k = \frac{\pi d^3/32}{\pi d^2/4} = \frac{d}{8}, \] which is the radius of the kernel.
Step 3: Convert radius to diameter.
\[ \text{Diameter of kernel} = 2k = 2 \times \frac{d}{8} = \frac{d}{4}. \]
\[ \boxed{\frac{d}{4}} \]