A cylindrical rod is subjected to a tensile force. If the radius of the rod is halved while keeping the length constant, how does the tensile stress change?
Practice Questions
1 question
Q1
A cylindrical rod is subjected to a tensile force. If the radius of the rod is halved while keeping the length constant, how does the tensile stress change?
It doubles
It halves
It quadruples
It remains the same
Tensile stress is given by force/area. Halving the radius reduces the area by a factor of four, thus the stress quadruples for the same force.
Questions & Step-by-step Solutions
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Q
Q: A cylindrical rod is subjected to a tensile force. If the radius of the rod is halved while keeping the length constant, how does the tensile stress change?
Solution: Tensile stress is given by force/area. Halving the radius reduces the area by a factor of four, thus the stress quadruples for the same force.
Steps: 8
Step 1: Understand that tensile stress is calculated using the formula: Tensile Stress = Force / Area.
Step 2: Identify that the area of a cylindrical rod is calculated using the formula: Area = π * (radius^2).
Step 3: Note that if the radius of the rod is halved, the new radius becomes (1/2) * original radius.
Step 4: Calculate the new area using the new radius: New Area = π * ((1/2) * original radius)^2.
Step 5: Simplify the new area: New Area = π * (1/4) * (original radius^2) = (1/4) * (π * (original radius^2)).
Step 6: Compare the new area to the original area: The new area is 1/4 of the original area.
Step 7: Since tensile stress is Force / Area, if the area decreases by a factor of 4, the tensile stress increases by a factor of 4 for the same force.
Step 8: Conclude that halving the radius of the rod while keeping the length constant causes the tensile stress to quadruple.
