CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
Question

A large steel wheel is to be fitted on a shaft of the same material. At 27 C, the outer diameter of the shaft is 8.70 cm and the diameter of the central hole of the wheel is 8.69 cm. The shaft is cooled using 'dry ice'. At what temperature of the shaft does the wheel slip on it?
[ α=1.20×105/ C ]

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

The correct option is C 69 C
Given:
At T1=27 C,
Outer diameter of the shaft, ds=8.70 cm
Diameter of central hole of the wheel, dw=8.69 cm
Co-efficient of linear expansion of steel, α=1.20×105/ C
Wheel will slip on the shaft when the outer diameter of the shaft becomes equal to diameter of the central hole of the wheel.
Let us suppose it becomes equal at temperature T2.
We know that,
L=L0[1+α(T2T1)]
dw=ds[1+α(T2T1)]
8.69=8.70[1+1.20×105(T227)]
T227=8.698.708.70×1.20×105=95.78 C
T269 C

flag
Suggest Corrections
thumbs-up
0
BNAT
mid-banner-image
similar_icon
Similar questions
View More