AP EAMCET201921 Apr 2019Morning ShiftPhysicsMechanical Properties of SolidsActual
The following four wires are made of the same material. If same tension is applied to each, the wire having largest extension is
Options
- Alength 0.5 m, diameter 0.5 mm.
- Blength 1 m, diameter 1 mm.
- Clength 2 m, diameter 2 mm.
- Dlength 3 m, diameter 3 mm.
Correct answer
A. length 0.5 m, diameter 0.5 mm.
Step-by-step solution
Given, that material is same, so Young's modulus = constant and tension = constant . Hence, the extension, aligned L & = F L Y A So, L & = 4 F Y L D^2 ( A= D^2 4 ) L & L D^2 aligned So, now checking the options, (a) aligned & L=0.5 ~m , D=0.5 ~mm =0.5 10⁻³ ~m & L= 4 F Y 0.5 (0.5 10⁻³ )^2 =2 10^6 4 F Y aligned (b) aligned L & =1 ~m , D=1 ~mm L & = 4 F Y 1.0 10^6 aligned (c) aligned L & =2 ~m , D=2 ~mm L & = 4 F Y 4 0.5 10^6 aligned (d) aligned L & =3 ~m , D=3 ~mm L & = 4 F Y 0.33 10^6 aligned Hence, 4 F Y is a const