Question

A bushy crop stem of diameter 6 mm is cut by bending. Modulus of elasticity = 1500 N·mm$^{-2}$, ultimate tensile strength = 35 N·mm$^{-2}$. Determine force causing failure at 50 mm height. (Take $\pi = 3.14$)
 

• A. 14.84
• B. 23.52
• C. 29.69
• D. 44.53

Hint:

For bending: $M = \sigma Z$, and $Z = I/c$ for circular cross-sections.

Answer 1

The Correct Option is A

Step 1: Compute section modulus.
Diameter $d = 6$ mm. \[ I = \frac{\pi d^4}{64} = \frac{3.14 \times 6^4}{64} = 63.62 \, \text{mm}^4. \] Section modulus: \[ Z = \frac{I}{d/2} = \frac{63.62}{3} = 21.21 \, \text{mm}^3. \]

Step 2: Bending moment at failure.
\[ \sigma = \frac{M}{Z} $\Rightarrow$ M = \sigma Z = 35 \times 21.21 = 742.35 \, \text{N·mm}. \]

Step 3: Force at 50 mm height.
\[ M = Fh $\Rightarrow$ F = \frac{M}{50} = \frac{742.35}{50} = 14.84 \, \text{N}. \]