Correct Answer - Option 1 : 1/3
Explanation:
Elongation of the prismatic bar due to self-weight:
\({{\bf{\delta }}_1} = \frac{{{\bf{\gamma }}{{\bf{l}}^2}}}{{2{\bf{E}}}}\)
Elongation of the conical bar due to self-weight:
\({{\bf{\delta }}_2} = \frac{{{\bf{\gamma }}{{\bf{l}}^2}}}{{6{\bf{E}}}}\)
Where,
γ = unit weight of the member
l = length of the member
E = young modulus of elasticity
Ratio of elongations of conical bar due to its own weight and that of prismatic bar:
\(\frac{{{{\bf{\delta }}_2}}}{{{{\bf{\delta }}_1}}} = \frac{{\frac{{{\bf{\gamma }}{{\bf{l}}^2}}}{{6{\bf{E}}}}}}{{\frac{{{\bf{\gamma }}{{\bf{l}}^2}}}{{2{\bf{E}}}}}}\)
\(\frac{{{{\bf{\delta }}_2}}}{{{{\bf{\delta }}_1}}} = \frac{1}{3}\)
