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A wooden wheel of radius R is made of two semi-circular parts

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A wooden wheel of radius $R$ is made of two semi-circular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L . L$ is slightly less than $2 π R$ . To fit the ring on the wheel, it is heated so that its temperature rises by $Δ T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semi-circular parts together. If the coefficient of linear expansion of the metal is $α$ and its Young's modulus is $Y$ , the force that one part of the wheel applies on the other part is

(a) $2 π S Y α Δ T$
(b) $S Y α Δ T$
(c) $π S Y α Δ T$
(d) $2 S Y α Δ T$

Views: 5,642 students

Updated on: Mar 7, 2023

Book:

Arihant Physics JEE Main Chapterwise Solutions (2019-2002) (Arihant)

Exam:

JEE Mains 2013

Found 2 tutors discussing this question

Liam Discussed

A wooden wheel of radius

R

is made of two semi-circular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area

S

and length

L . L

is slightly less than

2 π R

. To fit the ring on the wheel, it is heated so that its temperature rises by

Δ T

and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semi-circular parts together. If the coefficient of linear expansion of the metal is

α

and its Young's modulus is

Y

, the force that one part of the wheel applies on the other part is

(a)

2 π S Y α Δ T

(b)

S Y α Δ T

(c)

π S Y α Δ T

(d)

2 S Y α Δ T

12 mins ago

Discuss this question LIVE

12 mins ago

Text solutionVerified

E x p . (d)

Elongation due to change in temperature,
Solution Image

Δ l = Lα Δ T

which is compensated by elastic strain, when temperature becomes normal, i.e.,

Δ J = \frac{T L}{Y S}

Thus,

\frac{T L}{Y S} = Lα Δ T \Rightarrow T = V S α Δ T

At equilibrium, force exerted by one half on other,

F = 2 T = 2 Y S α Δ T

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Question Text	A wooden wheel of radius $R$ is made of two semi-circular parts (see figure). The two parts are held together by a ring made of a metal strip of cross-sectional area $S$ and length $L . L$ is slightly less than $2 π R$ . To fit the ring on the wheel, it is heated so that its temperature rises by $Δ T$ and it just steps over the wheel. As it cools down to surrounding temperature, it presses the semi-circular parts together. If the coefficient of linear expansion of the metal is $α$ and its Young's modulus is $Y$ , the force that one part of the wheel applies on the other part is (a) $2 π S Y α Δ T$ (b) $S Y α Δ T$ (c) $π S Y α Δ T$ (d) $2 S Y α Δ T$
Updated On	Mar 7, 2023
Topic	Thermal properties of Matter
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 4
Upvotes	380
Avg. Video Duration	8 min

Text solutionVerified

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