Question

A prismatic bar of rectangular cross- section is suspended freely from the ceiling of a roof. If all dimensions of the bar are doubled, then the total elongation produced by its own weight will increase by:

• A. 8 times
• B. 6 times
• C. 2 times
• D. 4 times

Answer 1

Answer:

D. 4 times

A prismatic bar's elongation due to self-weight is given by $\Delta L =\frac {\gamma L ^ 2}{2E}$ Doubling all dimensions of the bar increases its length to 2L. So, $\Delta L$ ∝ $L ^ 2$ Now $\frac{ (\Delta L) _2 }{( \Delta L)_1}$ =$\frac {L_ 2 ^ 2} {L _1 ^ 2} \Rightarrow \frac {(2L) ^ 2}{L ^ 2} = 4$