Two plate load tests on a cohesionless soil yielded the following data:

a$)$ Determine the stress$-$strain modulus Es of the supporting soil. Assume the soil Poisson's ratio $=0\mathrm{.}35.$

b$)$ What will be the differential settlement of two footings, one of the size $2\mathrm{.}5m2\mathrm{.}5m,$ supporting a column load of $700$ kN $,$ the other of the size $3\mathrm{.}0$ m $3\mathrm{.}0m,$ supporting a column load of $1000$ kN $?$ Assume the footings are so apart that there will be no overlap of stresses take place in the supporting soil. Take $I=0\mathrm{.}82($for centre$).$

$\backslash$table$[[$Plate size, m$,$Load V$,$ kN$,s_{\text{p}\text{l}\text{a}\text{t}\text{e}\text{,}},mm$