List of practice Questions

Given that \(\vec{F}(x,y,z)=\sin(y)\,\hat{x}+\cos(x)\,\hat{y}+5\,\hat{z}\), the integral \(\oiint_S \vec{F}(x,y,z)\cdot d\vec{s}\) over the unit sphere \(S\) centered at the origin evaluates to
(Round off to one decimal place)
Proctor's compaction test for the maximum dry density of a certain soil gave the results as $1.8 \text{ gm/cc}$ and Optimum Moisture Content (OMC) is $15%$. The specific gravity of the clay soil grain was 2.7. What was the saturation degree for this soil?
Which structural element ideally carries only axial forces?

The value of $\iint_S \vec{F} \cdot \vec{N} \, ds$ where $\vec{F} = 2x^2y \hat{i} - y^2 \hat{j} + 4xz^2 \hat{k}$ and $S$ is the closed surface of the region in the first octant bounded by the cylinder $y^2 + z^2 = 9$ and the planes $x = 0, x = 2, y = 0, z = 0$, is: