Q: 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 w

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

Question 1

Match List I with List II : List I List II A. Young's Modulus I. d L ( L d ) B. Compressibility II. F L A( L) C. Bulk Modulus III. - 1 P ( V V ) D. Poisson's Ratio IV. -P ( V V ) Choose the correct an

Accepted Answer

Young's Modulus is the ratio of longitudinal stress to longitudinal strain: Y = F/A L/L = FL A L This matches A with II. Compressibility is the reciprocal of Bulk Modulus: k = 1 B = - V/V P = - 1 P ( V V ) This matches B with III. Bulk Modulus is the ratio of volumetric stress to volumetric strain: B = -P V/V = -P ( V V ) This matches C with IV. Poisson's Ratio is the ratio of lateral strain to longitudinal strain: = d/d L/L = d L ( L d ) This matches D with I. The correct matching is A-II, B-II

Question 2

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 w

Accepted Answer

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

Question 3

The maximum elongation of a steel wire of 1 m length if the elastic limit of steel and its Young's modulus, respectively, are 8 10^8 ~N ~m ^ -2 and 2 10^ 11 ~N ~m ^ -2 , is:

Accepted Answer

In the case for maximum elongation, Stress = Elastic limit aligned _ = _ elastic L Young's modulus = 8 10^8 1 2 10^ 11 & =4 10^ -3 \ & =4 ~mm aligned i.e. maximum elongation is 4 mm

Mechanical Properties of Solids — Previous Year Questions & Solutions