A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lower end. If its radius is r, its length L and the Young's modulus for the material of the wire is E, the extension is 1. directly proportional to E 2. inversely proportional to r 3. directly proportional to L

Question

A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lower end. If its radius is r, its length L and the Young's modulus for the material of the wire is E, the extension is 1. directly proportional to E 2. inversely proportional to r 3. directly proportional to L (A) if only 3 is correct (B) if 1,2 are correct (C) if 2,3 are correct (D) if only 1 is correct

Tardigrade Admin · Accepted Answer

As, E=(F L/π r2 Δ L) or Δ L=(F L/π r2 E) Clearly, Δ L propto L

Q. A uniform wire, fixed at its upper end, hangs vertically and supports a weight at its lower end. If its radius is r, its length L and the Young's modulus for the material of the wire is E, the extension is 1. directly proportional to E 2. inversely proportional to r 3. directly proportional to L

if only 3 is correct

if 1,2 are correct

if 2,3 are correct

if only 1 is correct

As, E=πr2ΔLFL​ or ΔL=πr2EFL​ Clearly, ΔL∝L

As, $E = \frac{F L}{π r ^{2} Δ L}$
or $Δ L = \frac{F L}{π r ^{2} E}$
Clearly, $Δ L \propto L$