Question: What is the relationship between the stiffness (k) of a beam and its moment of inertia (I)?
Options:
k ∝ I
k ∝ 1/I
k ∝ I^2
k ∝ √I
Correct Answer: k ∝ I
Solution:
The stiffness (k) of a beam is directly proportional to its moment of inertia (I), meaning k ∝ I.
What is the relationship between the stiffness (k) of a beam and its moment of i
Practice Questions
Q1
What is the relationship between the stiffness (k) of a beam and its moment of inertia (I)?
k ∝ I
k ∝ 1/I
k ∝ I^2
k ∝ √I
Questions & Step-by-Step Solutions
What is the relationship between the stiffness (k) of a beam and its moment of inertia (I)?
Step 1: Understand what stiffness (k) means. Stiffness is how much a beam resists bending when a force is applied.
Step 2: Learn about moment of inertia (I). Moment of inertia is a measure of how the mass of the beam is distributed relative to an axis, affecting how it bends.
Step 3: Recognize the relationship. When the moment of inertia (I) increases, the beam becomes stiffer (k) and resists bending more.
Step 4: Conclude that stiffness (k) is directly proportional to moment of inertia (I). This means if I goes up, k goes up too.
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