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Prove `S_r *e=w*G`.

We know, the void ratio,e, is defined as a ratio of volume of voids to the volume of solid particles.

`e=V_v/V_s`

  `=(V_v/V_w )*(V_w/V_s)`

  `=(V_v/V_w)*((W_w/gamma_w)/(W_s/gamma_s))`

  `=(V_v/V_w )*(W_w/W_s)*(gamma_s/gamma_w)`

We know,

Specific gravity,`G=gamma_s/gamma_w`

Thus,`e=(V_v/V_w)*(W_w/W_s)*G`

      `=(1/S_r)*w*G`

Or, `S_r *e=w*G`

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