Question

The elongation of a conical bar of length L under the action of its own weight is ___ that of a prismatic bar of the same length.

• A. One half
• B. One third
• C. One fourth
• D. Equal to length

Hint:

When solving problems related to elongation and deformation, ensure to consider the shape and properties of the object (conical, prismatic) and use the correct formula for elongation.

Answer 1

The Correct Option is B

The elongation of a conical bar under the action of its own weight is given by the formula:
\[ \Delta L = \frac{4}{3} \times \frac{F L}{A \sigma} \] Where:
- \( F \) is the weight,
- \( L \) is the length,
- \( A \) is the cross-sectional area,
- \( \sigma \) is the stress.
When compared with a prismatic bar of the same length, the elongation of a conical bar is one-third of that of a prismatic bar. Hence, the correct answer is "One third".