(Solved): Starting with the basic definition of unit weight, derive the following relationships using the bas ...

Starting with the basic definition of unit weight, derive the following relationships using the basic weight-volume relations. a) \( \gamma=\left[(1+\omega) \mathrm{G}_{\mathrm{s}} \gamma_{\mathrm{w}}\right] /(1+\mathrm{e}) ; \) Assume \( \mathrm{V}_{\mathrm{s}} \neq 1 \) b) \( \quad \gamma_{\mathrm{d}}=\mathrm{G}_{\mathrm{s}} \gamma_{\mathrm{w}} /(1+\mathrm{e}) ; \) Assume \( \mathrm{V}_{\mathrm{s}} \neq 1 \) c) \( \quad \gamma_{\text {sat }}=\left[\left(\mathrm{G}_{\mathrm{s}}+\mathrm{e}\right) \gamma_{\mathrm{w}}\right] /(1+\mathrm{e}) ; \) Assume \( \mathrm{V}_{\mathrm{s}}=1 \)