A uniform, slender cylindrical rod is made of a homogeneous and isotropic material. The rod rests on a frictionless surface. The rod is heated uniformly. If the radial and longitudinal thermal stresses are represented by $\sigma_r$ and $\sigma_z$, respectively, then
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$\sigma_r=0,\sigma_z=0$
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$\sigma_r\neq0,\sigma_z=0$
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$\sigma_r=0,\sigma_z\neq0$
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$\sigma_r\neq0,\sigma_z\neq0$
A
Correct answer
Explanation
$\text {We know that due to temperature changes, dimensions of the material change.}\\
\text{ If these changes in the dimensions are prevented partially or fully,stresses are generated in the material and if the changes in the dimensions are not prevented, there will be no stress set up.(Zero stresses).}\\
\text{ Hence cylindrical rod is allowed to expand or contract freely.} \\
So \sigma_r=0and \sigma_z=0$