Properties Of Solids And Liquids Question 535

Question: At $ 15{}^\circ C, $ a wheel has diameter of 30 cm and inside diameter of a steel rim is 29.9 cm. Coefficient of thermal expansion of steel is $ 1.2\times {{10}^{-5}}{{/}^{o}}C $ . To what temperature, the rim must be heated so that it can slip over wheel?

Options:

A) $ 2787{}^\circ C $

B) $ 2772{}^\circ C $

C) $ 2529{}^\circ C $

D) $ 2802{}^\circ C $

Show Answer

Answer:

Correct Answer: D

Solution:

Rim will slip if its diameter increases to 30 cm. Hence $ \Delta l=0.1cm $

$ \Delta T=\frac{\Delta l}{l\times a}=\frac{0.1}{29.9\times 1.2\times {{10}^{-5}}}=2787^{o}C $

Rim to be heated to temperature

$ 2787+15=2802^{o}C $



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