Q

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

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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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