KCET2024PhysicsMechanical Properties of Solids
A thick metal wire of density and length L is hung from a rigid support. The increase in length of the wire due to its own weight is ( Y= Young's modulus of the material of the wire)
Options
- Ag L Y
- B1 2 g L^2 Y
- Cg L^2 Y
- D1 4 Y g L^2
Correct answer
B. 1 2 g L^2 Y
Step-by-step solution
Weight of the metal wire, w=m g Longitudinal stress = W A = m g A Y= Longitudinal stress Longitudinal strain = m g A l ( l 2 ) [ . Weight of the wire acts at its centre . L^ = L 2 ] l= m g l 2 Y A = m A L L^2 g 2 Y = L^2 g 2 Y