SATHEE: Properties Of Solids And Liquids Question 398

Properties Of Solids And Liquids Question 398

Question: An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is $3.6 \times 10^{- 5})$

Options:

A) $167^{\circ} C$

B) $334^{\circ} C$

C) $500^{\circ} C$

D) $1000^{\circ} C$

Show Answer

Answer:

Correct Answer: C

Solution:

[c] Initial diameter of tyre =(1000 - 6) mm =994 mm,

so initial radius of tyre $R = \frac{994}{2} = 497 m m$ and change in diameter $Δ D = 6 m m$ so $Δ R = \frac{6}{2} = 3 m m$

After increasing temperature by $Δ θ$ tyre will fit onto wheel Increment in the length (circumference) of the iron tyre $Δ L = L \times α \times Δ θ = L \times \frac{γ}{3} \times Δ θ [A s α = \frac{γ}{3}]$

$2 π Δ R = 2 π R (\frac{γ}{3}) Δ θ \Rightarrow Δ θ$

$= \frac{3}{γ} \frac{Δ R}{R} = \frac{3 \times 3}{3.6 \times 10^{- 5} \times 497} \Rightarrow Δ θ ≃ 500^{o} C$

Properties Of Solids And Liquids Question 398

Question: An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is $3.6 \times 10^{- 5})$

Options:

Answer:

Solution:

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Properties Of Solids And Liquids Question 398

Question: An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is 3.6×10−5)

Options:

Answer:

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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Question: An iron tyre is to be fitted on to a wooden wheel 1m in diameter. The diameter of tyre is 6 mm smaller than that of wheel. The tyre should be heated so that its temperature increases by a minimum of (the coefficient of cubical expansion of iron is $3.6 \times 10^{- 5})$