wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A steel wire of cross sectional area 0.05 cm2 is under a tension of 15 N. Find the decrease in the cross-sectional area. Young's modulus of steel = 2×1011N/m2 and Poisson's ratio = 0.3.

A
40×108cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
50×108cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
45×108cm2
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
22.5×108cm2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 45×108cm2
Let d be the diameter of steel wire and L be the length of wire.
So, Poisson ratio (ν)=0.3=ΔddΔLL
Now, Stress (σ)=FA=150.05×104=300×104 N/m2
Young's modulus (Y)=σΔLL
ΔLL=σY=300×1042×1011=1.5×105
Now, ν=ΔddΔLL=Δdd1.5×105
0.3=Δdd1.5×105
Δdd=0.3×1.5×105=0.45×105
Now, ΔAA=2Δdd=0.9×105
ΔA=0.9×105×A=0.9×0.05×105=0.045×105 m2
ΔA=45×108cm2

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon