QJEEM17Ph0ea6: JEE Main 2017 Physics - Class 11 JEEM17Ph0ea6 Solution: A compressive force, F is applied at the two ends of a long…

Question

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A compressive force, F is applied at the two ends of a long thin steel rod. It is heated, simultaneously, such that its temperature increases by

Δ

T. The net change in its length is zero. Let

ℓ

be the length of the rod, A its area of cross-section,Y its Young’s modulus, and

α

its coefficient of linear expansion. Then, F is equal to :

Accepted Answer

Because of thermal expansion, change in length

(

Δ

ℓ

) =

ℓ

α

Δ

T . . . . .(1)

Because of compressive force, the compansion is

Δ

ℓ

' ,

∴

Young's Modulus (y) =

\frac{\frac{F}{A}}{\frac{Δ ℓ}{ℓ}}

\Rightarrow

F = YA

\frac{Δ ℓ^{'}}{ℓ}

As net change in length is 0 . So,

Δ ℓ^{'}

=

Δ ℓ

=

ℓ α Δ T

∴

F = YA

\times

\frac{ℓ α Δ T}{ℓ}

= AY

α

Δ

T

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