Discussion Forum

 The pressure  that has to be applied in the ends of a steel wire of length  10cm to keep its length  constant  when  its temperature is raised by 100° C  is (For  steel, Young's modulus  is   $2\times 10^{11}Nm^{-2}$ and coefficient of thermal expansion is $1.1\times 10^{-5}K^{-1}$ )

Answer:

Explanation:

 If the deformation is small, then the stress ina body is directly proportional to the corresponding strain.

 According to Hooke's law, i,e

 Young's modulus (Y)= Tensile stress/ Tensile strain

 So, $Y= \frac{F/A}{\triangle L/L}=\frac{FL}{A\triangle L}$

 If the rod is compressed, then compressive stress and strain appear. Their ratio Y is same as that for tensile case.

 Given, length  of stress wire (L)=10cm

   Temperature (Θ)=100⁰C

 As length is constant.

$\therefore$   Strain=  $\frac{\triangle L}{L}==\alpha \triangle \theta$

  Now, pressure=stress

     = Y x strain

 [Given,   $Y=2\times 10^{11}N/m^{2}$    and   $\alpha=1.1\times10^{-5}K^{-1}$]

$=2\times 10^{11}\times1.1\times 10^{-5}\times100$

  $=2.2\times 10^{8}Pa$