Question Bank • QB_SWCE_ADV_114 MSQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Soil Mechanics

Subtopic: Fundamental definitions and relationships

Question Statement:

Which of the following mathematical equations correctly express interrelationships between unit weights, void ratio ($e$), moisture content ($w$), and specific gravity ($G_s$) in soil mechanics?

Options:

  • (A) Dry unit weight: $\gamma_d = \frac{\gamma}{1 + w}$
  • (B) Dry unit weight: $\gamma_d = \frac{G_s \gamma_w}{1 + e}$
  • (C) Saturated unit weight: $\gamma_{sat} = \frac{(G_s + e)\gamma_w}{1 + e}$
  • (D) Submerged unit weight: $\gamma' = \frac{(G_s - 1)\gamma_w}{1 + e}$

Answer Key:

A, B, C, D

Step-by-Step Solution & Explanation

All four relationships are canonical exact identities: - A: $\gamma_d = \frac{\gamma}{1 + w}$ relates bulk and dry unit weights. - B: $\gamma_d = \frac{W_s}{V} = \frac{G_s \gamma_w V_s}{(1 + e)V_s} = \frac{G_s \gamma_w}{1 + e}$. - C: At $S_r = 1$, $\gamma_{sat} = \frac{(G_s + S_r e)\gamma_w}{1 + e} = \frac{(G_s + e)\gamma_w}{1 + e}$. - D: $\gamma' = \gamma_{sat} - \gamma_w = \frac{(G_s + e)\gamma_w - (1 + e)\gamma_w}{1 + e} = \frac{(G_s - 1)\gamma_w}{1 + e}$.
← Previous (QB_SWCE_004) Next (QB_SWCE_EXP_018) →

Practice In Authentic CBT Exam Interface

Test your skills under authentic timed conditions with live scoring and AIR percentile ranking.

Launch CBT Mock Test