Question

A mild steel bar is in two parts having equal length. The area of cross-section of part-1 is double that of part-2. If the bar carries an axial load P, then the ratio of elongation in part-1 to that in part-2 will be
1. 2
2. 4
3. 1/2
4. 1/4

Answer 1

Correct Answer - Option 3 : 1/2

Concept:

Elongation (δ) of

 a bar under tensile load is given by,

\(\delta = \frac{{PL}}{{AE}}\)

Calculation:

Given;

A₁ = 2A₂

Elongation for part -1;

\(\delta_1 = \frac{{PL}}{{A_1E}}\)

Elongation for part -2;

\(\delta_2 = \frac{{PL}}{{A_2E}}\)

So,

\(\frac{{{\delta _1}}}{{{\delta _2}}} = \left( {\frac{{\frac{{PL}}{{{A_1}E}}}}{{\frac{{PL}}{{{A_2}E}}}}} \right) = \left( {\frac{{{A_2}}}{{{A_1}}}} \right) = \left( {\frac{{{A_2}}}{{2{A_2}}}} \right)\)

\(\frac{{{\delta _1}}}{{{\delta _2}}} = \frac{1}{2}\)