Question

According to Metzer’s theory, the stem of the tree is built up in such a way as, with the minimum of material, to offer uniformly the greatest resistance to the stresses to which it is subjected.

• A. A only
• B. B only
• C. C only
• D. D only

Hint:

Metzger's Theory = Optimization. Think of a tree like a skyscraper; it's wide at the base and narrow at the top to handle wind without using extra weight.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
Metzger's theory (1893), also known as the "Beam Theory," explains why tree stems have a specific tapered shape. It applies engineering principles to biological growth.

Step 2: Detailed Explanation:

• The Core Concept: Metzger proposed that a tree stem acts as a cantilever beam anchored in the ground. The primary stress it faces is wind pressure acting on the canopy.

• Structural Efficiency: The theory states that a tree allocates its wood (biomass) in a way that provides maximum structural integrity with the minimum amount of material. It is nature's version of "optimal design."

• Stress Distribution: To withstand wind loads, the bending moment is greatest at the base and decreases towards the top. Therefore, the stem must be thicker at the bottom. Metzger's theory suggests the stem's cross-sectional area at any point is proportional to the bending moment at that point, creating a taper that ensures uniform resistance to stress.

• Statement A analysis: Matches the established definition of Metzger’s theory perfectly. It emphasizes "minimum material" and "uniform greatest resistance."

• Other Statements (B, C, D): These typically vary the terms "maximum material" or "equal resistance," which are deviations from the original optimization principle proposed by Metzger.

Step 3: Final Answer:
Statement A is the only accurate description of Metzger’s theory.