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Please,please help me Two rods A and B of identical dimensions are at temperature 30oC . If A is heated upto 180 oC and B upto ToC , then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4:3 , then the value

Two rods A and B of identical dimensions are at temperature 30oC . If A is heated upto 180 oC and B upto ToC , then the new lengths are the same. If the ratio of the coefficients of linear expansion of A and B is 4:3 , then the value of T is :

  • Option 1)

    270oC

  • Option 2)

    230oC

  • Option 3)

    250oC

  • Option 4)

    200oC

Answers (1)
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A admin

 

Coefficient of Linear Expansion -

\alpha=\frac{\Delta L}{L_{0}\Delta T}

- wherein

Unit of \alpha is C-1 or  K-1

 

A                               B

T_{o}=30\: \: \: \: \: \: \: \: \: T_{o}=30

T_{f}=180\: \: \: \: \: \: \: \: \: T_{f}=T

\alpha _{A}\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \:\: \: \: \: \: \: \: \alpha _{B}

\frac{\alpha _{A}}{\alpha _{B}}=\frac{4}{3}

\bigtriangleup l_{1}=\bigtriangleup l_{2}

l\alpha _{A}\bigtriangleup T_{A}=l\alpha _{B}\bigtriangleup T_{B}

\frac{\alpha _{A}}{\alpha _{B}}=\frac{4}{3}=\frac{\bigtriangleup T_{B}}{\bigtriangleup T_{A}}=\frac{\left ( T-30 \right )}{\left ( 180-30 \right )}

T-30=\frac{4}{3}\times 150

T=30+200

T=230^{\circ}C


Option 1)

270oC

Option 2)

230oC

Option 3)

250oC

Option 4)

200oC

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