A metallic bar of Young's modulus, 0.5 10^ 11 ~N ~m ^ -2 and coefficient of linear thermal expansion 10^ -5 ^ C ^ -1 , length 1 m and area of cross-section 10^ -3 ~m ^2 is heated from 0^ C to 100^ C without expansion or bending. The compressive force developed in it is :
A. 50 10^3 ~N
aligned & Thermal strain = Longitudinal strain = T \\ & Longitudinal strain, =10^ -5 10^2=10^ -3 \\ & Compressive stress = Young's Modulus \\ & =10^ -3 0.5 10^ 11 \\ & =0.5 10^8 \\ & Compressive force =0.5 10^8 10^ -3 =0.5 10^5 \\ & =5 10^4 10 10 \\ & =50 10^3 ~N aligned
Related: Physics — Mechanical Properties of Solids · All PYQ Banks