A metal rod of length ‘L’ and cross-sectional area ‘A’ is heated through ‘T’ °C. What is the force required to prevent the expansion of the rod lengthwise ? [Y = Young's modulus of the material of rod , α = coefficient of linear expansion]

Question

A metal rod of length ‘L’ and cross-sectional area ‘A’ is heated through ‘T’ °C. What is the force required to prevent the expansion of the rod lengthwise ? [Y = Young's modulus of the material of rod , α = coefficient of linear expansion] (A) (Y A α T/(1 - α T)) (B) (Y A α T/(1 + α T)) (C) ((1 - α T)/Y A α T) (D) ((1 + α T)/Y A α T)

Tardigrade Admin · Accepted Answer

change in length δ L = L α T final length L f = L +δ L now in order to to constrain the expansion, there should be force that should compress the rod by δ L strain =(δ L / L f ) Y =( F / A / text strain ) F =( YA A T /1+α T )

Q. A metal rod of length ‘ $L$ ’ and cross-sectional area ‘ $A$ ’ is heated through $‘ T ’^{\circ} C$ . What is the force required to prevent the expansion of the rod lengthwise ?
[ $Y =$ Young's modulus of the material of rod , $α$ = coefficient of linear expansion]

$\frac{Y A α T}{( 1 - α T )}$

$\frac{Y A α T}{( 1 + α T )}$

$\frac{( 1 - α T )}{Y A α T}$

$\frac{( 1 + α T )}{Y A α T}$

change in length $δ L = Lα T$
final length $L_{f} = L + δ L$
now in order to to constrain the expansion,
there should be force that should compress the rod by $δ L$
strain $= \frac{δ L}{L _{f}}$
$Y = \frac{F / A}{strain}$
$F = \frac{Y AA T}{1 + α T}$

Q. A metal rod of length ‘L’ and cross-sectional area ‘A’ is heated through ‘T’∘C. What is the force required to prevent the expansion of the rod lengthwise ? [Y= Young's modulus of the material of rod , α = coefficient of linear expansion]

(1−αT)YAαT​

(1+αT)YAαT​

YAαT(1−αT)​

YAαT(1+αT)​