Question

The high domes of ancient buildings have structural value (besides beauty). It arises from pressure difference on the two faces due to curvature (as in soap bubbles). There is a dome of radius 5 m and uniform (but small) thickness. The surface tension of its masonry structure is about 500 N/m. Treated as hemispherical, the maximum load the dome can support is nearest to

• A. 1500 kg wt.
• B. 3000 kg wt.
• C. 6000 kg wt.
• D. 12000 kg wt.

Answer 1

Answer: (B)

3000 kg wt.

$\begin{array}{c}{P}_{\text{ext}}=\frac{4T}{R}\\ \text{Max. Load that can be supported}\\ \begin{array}{cc}F& =P_{ext}\times \pi r^2\\ & =\frac{4T}{R}\times \pi R^2=4T\times \pi R\end{array}\end{array}$

$\begin{array}{cc}F& =4\times 500\times \frac{22}{7}\times 5\\ & =2000\times 5\times \frac{22}{7}=31400N\\ F\text{in}kg\omega t=\frac{31400}{g}N\approx 3000& ,\therefore \text{Option (B) is correct}\end{array}$