Question

There are two steel rods, one has three times the area and twice the length of the first, are under the action of the same force. Find the ratio of the extension of the two rods.

Answer 1

To find the ratio of the extension of two steel rods, use the equation for elongation: ΔL = (FL)/(AY). Assuming the same force is applied, the ratio of their extensions is equal to the ratio of their cross-sectional areas.

Step-by-step explanation:

To find the ratio of the extension of the two rods, we can use the equation for elongation: ΔL = (FL)/(AY), where ΔL is the change in length, F is the force applied, A is the cross-sectional area of the rod, and Y is the Young's modulus of the material.

For the first rod, let's denote its area as A1 and length as L1. For the second rod, its area is 3A1 and length is 2L1. Assuming the same force is applied to both rods, the ratio of their extensions can be calculated as:

(ΔL2 / L2) / (ΔL1 / L1) = ((F / (A2 * Y)) / (2L1)) / ((F / (A1 * Y)) / L1) = (2A1 / A2)