# A large steel whe

Given,

Initial temperature, T1 = 27°C = 27 + 273.15 = 300.15 K

Outer diameter of the steel shaft at T1, D1 = 8.70 cm

Diameter of the central hole in the wheel at T1, d1 = 8.69 cm

Coefficient of linear expansion of steel, αsteel = 1.20 × 10-5 K-1

Let the temperature be T2 after the shaft is cooled using ‘dry ice’.

The wheel will slip on the shaft, if the change in diameter,

Δd = 8.69 – 8.70 = – 0.01 cm

Temperature T2 can be calculated as follows.

Δd = D1αsteel(T2 – T1)

-0.01 cm = 8.70 cm × 1.20 × 10-5 K-1 × (T2 – 300.15 K)

(T2 – 300.15 K) = -95.78 K

T2 = 204.37 K = 204.37 – 273.15 = -68.78°C

Therefore, the wheel will slip on the shaft when the temperature of the shaft is –68.78°C.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses
RELATED QUESTIONS :

Calculate the strPhysics - Exemplar

We would like to Physics - Exemplar

<span lang="EN-USPhysics - Exemplar

We would liPhysics - Exemplar

A thin rod havingPhysics - Exemplar

Answer the followNCERT - Physics Part-II

A brass rod of leNCERT - Physics Part-II

Two ideal gas theNCERT - Physics Part-II

Answer the followNCERT - Physics Part-II

A brass wire 1.8 NCERT - Physics Part-II