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

A steel scale measures the length of a copper wire as 80.0 cm when both are at 20C (the calibration temperature for the scale). What would be the scale reading for the length of the wire when both are at 40C? (Given αsteel=11×106/ C and αcopper=17×106/ C)

A
80.0096 cm
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
B
80.0272 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
1 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
25.2 cm
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is A 80.0096 cm
Let the length of steel scale and copper wire at 20C be L0 .
For a change in temperature (ΔT), the length of a material changes to the new length given by, L=L0(1+α ΔT)
For steel scale,
New length due to change in temperature is given by
Lsteel=L0(1+αsteel ΔT) ......(1)
For copper wire,
New length due to change in temperature is given by
LCu=L0(1+αcu ΔT) ......(2)

The relative expansion of the copper wire w.r.t. steel scale after rise in temperature is given by
Lapp=LCuLsteel=[L0(1+αCuΔT)L0(1+αsteelΔT)]
[ Using (1) and (2) ]
Lapp=L0(αcuαsteel)ΔT
Change in temperature (ΔT)=4020=20C
Lapp=80×(17×10611×106)×20=0.0096 cm
Hence, the new length of the wire measured at 40 C
=L0+Lapp
=80.0096 cm
Hence, option (a) is the correct answer.

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