Exams › JEE Advanced › Physics
A rod of length L0, cross-sectional area A, and Young's modulus Y is connected to a spring of spring constant k (initially unstretched). The rod has linear thermal expansion coefficient alpha. When the rod's temperature is raised by delta_T, find the thermal stress developed in the rod.
- k*Y*alpha*delta_T*L0 / (k*L0 + Y*A)
- Y*alpha*delta_T
- (k*L0 + Y*A) / (k*L0) * Y*alpha*delta_T
- (k*L0 + Y*A) / (k*L0) * Y*alpha*delta_T
Correct answer: k*Y*alpha*delta_T*L0 / (k*L0 + Y*A)
Solution
Without the spring, the rod would expand by alpha*delta_T*L0 freely. With the spring, actual expansion x is less. Force equilibrium gives the actual extension, and the compressive stress equals k*x/A = k*Y*alpha*delta_T*L0/(k*L0 + Y*A).
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