MHT CET2019Evening ShiftPhysicsMechanical Properties of SolidsActual
A wire of length ‘L’ and area of cross section ‘A’ is made of material of Young’s modulus ‘Y’. It is stretched by an amount ‘x’. The work done in stretching the wire is
Options
- AY x 2 A 2 L
- B2 Y x 2 A L
- CY x A 2 L
- DY x 2 A 2
Correct answer
A. Y x 2 A 2 L
Step-by-step solution
If a force F is applied along the length L of wire for stretching by an amount x, then Young’s modulus is given by Y = s t r e s s s t r a i n = F L A x where, A = area of cross-sectional ⇒ F = Y A L x The work done is stretching the wire is given by W = ∫ 0 x F . d x = ∫ 0 x Y A L x = Y A L x 2 2 0 = Y A x 2 2 L