A cylindrical rod is subjected to a tensile force. If the diameter of the rod is
Practice Questions
Q1
A cylindrical rod is subjected to a tensile force. If the diameter of the rod is doubled while keeping the length constant, what happens to the stress in the rod?
Increases
Decreases
Remains the same
Becomes zero
Questions & Step-by-Step Solutions
A cylindrical rod is subjected to a tensile force. If the diameter of the rod is doubled while keeping the length constant, what happens to the stress in the rod?
Step 1: Understand what stress is. Stress is the force applied to an object divided by the area over which the force is applied.
Step 2: Identify the formula for stress: Stress = Force / Area.
Step 3: Note that the area of a circle (which is the cross-section of the cylindrical rod) is calculated using the formula: Area = π * (radius^2).
Step 4: If the diameter of the rod is doubled, the radius also doubles. If the original radius is r, the new radius becomes 2r.
Step 5: Calculate the new area using the new radius: New Area = π * (2r)^2 = π * (4r^2) = 4 * (π * r^2). This means the area increases by a factor of 4.
Step 6: Since the force applied to the rod remains the same, we can now compare the old and new stress values.
Step 7: The old stress = Force / (π * r^2). The new stress = Force / (4 * π * r^2).
Step 8: Compare the two stress values: New Stress = Old Stress / 4. This shows that the new stress is one-fourth of the old stress.
Step 9: Conclude that doubling the diameter of the rod reduces the stress in the rod.
Stress – Stress is defined as the force applied per unit area of a material.
Area Calculation – The area of a circle is calculated using the formula A = π(d/2)², where d is the diameter.
Effect of Diameter on Area – Doubling the diameter of a cylindrical rod increases the cross-sectional area by a factor of four.
