Question

A Steel wire having length 8 m and
diameter 4 mm is fixed between two rigid support. Calculate
increase in tension on a wire when temperature falls by
10°C. Where Young's modulus of wire = 2x1011 N/m2, linear
expansivity of steel = 1.2x10-5K-1.
​

Answer 1

Answer:

Given : Y=21×10

11

dyn/cm

2

α=12×10

−6

/

o

C

Change in temperature ΔT=20

o

C

Cross-section area of the wire A=0.5mm

2

=0.005cm

2

Using ΔL=LαΔT

⟹ Strain =

L

ΔL

=αΔT=12×10

−6

×20=2.4×10

−4

From Hooke's law, Stress=Y×Strain

⟹ Tension T=Y×Strain×A

∴ T=21×10

11

×2.4×10

−4

×0.005=252×10

4

dyn

⟹ T=25.2N (1N=10

5

dyn)