MCQOPTIONS

Explore topic-wise MCQs in Soil Mechanics.

This section includes 15 Mcqs, each offering curated multiple-choice questions to sharpen your Soil Mechanics knowledge and support exam preparation. Choose a topic below to get started.

1.	The partial differential of normal stress in y-direction in terms of effective stress is given by __________
A.	\(\frac{∂σ_y{‘}}{∂y}\)
B.	\(\frac{∂σ_y{‘}}{∂y}-γ_w \frac{∂h}{∂y}\)
C.	\(\frac{∂σ_y{‘}}{∂y}+γ_w \frac{∂h}{∂y}\)
D.	\(\frac{∂σ_y{‘}}{∂y}*γ_w \frac{∂h}{∂y}\)
Answer» D. \(\frac{∂σ_y{‘}}{∂y}*γ_w \frac{∂h}{∂y}\)

2.	The partial differential of normal stress in x-direction in terms of effective stress is given by __________
A.	\(\frac{∂σ_x{‘}}{∂x}\)
B.	\(\frac{∂σ_x{‘}}{∂x}-γ_w \frac{∂h}{∂x}\)
C.	\(\frac{∂σ_x{‘}}{∂x}+γ_w \frac{∂h}{∂x}\)
D.	\(\frac{∂σ_x{‘}}{∂x}*γ_w \frac{∂h}{∂x}\)
Answer» D. \(\frac{∂σ_x{‘}}{∂x}*γ_w \frac{∂h}{∂x}\)

3.	The normal stress in z-direction in terms of effective stress is given by __________
A.	σz= γw(h-he)
B.	σz= σz’
C.	σz= σz’+γw(h-he)
D.	σz= σz’-γw(h-h
E.	σz= σz’c) σz= σz’+γw(h-he)d) σz= σz’-γw(h-he)
Answer» D. σz= σz’-γw(h-h

4.	The normal stress in y-direction in terms of effective stress is given by __________
A.	σy= σy’-γw(h-he)
B.	σy= σy’+γw(h-he)
C.	σy= σy’/γw(h-he)
D.	σy= σy’*γw(h-h
E.	σy= σy’+γw(h-he)c) σy= σy’/γw(h-he)d) σy= σy’*γw(h-he)
Answer» C. σy= σy’/γw(h-he)

5.	The normal stress in x-direction in terms of effective stress is given by __________
A.	σx= σx’+γw(h-he)
B.	σx= σx’*γw(h-he)
C.	σx= σx’-γw(h-he)
D.	σx= σx’
E.	σx= σx’*γw(h-he)c) σx= σx’-γw(h-he)d) σx= σx’
Answer» B. σx= σx’*γw(h-he)

6.	The equilibrium equations in terms of total stresses formed by summing all forces on z-direction is ________
A.	\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +Z=0\)
B.	\(\frac{∂τ_{xy}}{∂x}+\frac{∂σ_y}{∂y}+\frac{∂τ_{zy}}{∂z}=0\)
C.	\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +γ=0\)
D.	\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)
Answer» D. \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)

7.	The equilibrium equations in terms of total stresses formed by summing all forces on y-direction is ________
A.	\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
B.	\(\frac{∂τ_{xy}}{∂x}+\frac{∂σ_y}{∂y}+\frac{∂τ_{zy}}{∂z}=0\)
C.	\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)
D.	\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)
Answer» C. \(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)

8.	The equilibrium equations in terms of total stresses formed by summing all forces on x-direction is ________
A.	\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
B.	\(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)
C.	\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)
D.	\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)
Answer» E.

9.	The three equations of static equilibrium of the problem of elasticity are not sufficient to solve the six unknown stress components.
A.	True
B.	False
Answer» B. False

10.	The problem of elasticity is _________
A.	strictly determinate
B.	strictly indeterminate
C.	in some cases indeterminate
D.	cannot be classified as determinate or indeterminate
Answer» C. in some cases indeterminate

11.	The equilibrium equation obtained by summing all forces on z-direction is ________
A.	\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
B.	\(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)
C.	\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)
D.	\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)
Answer» D. \(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)

12.	The equilibrium equation obtained by summing all forces on y-direction is ________
A.	\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
B.	\(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)
C.	\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)
D.	\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)
Answer» C. \(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)

13.	The equilibrium equation obtained by summing all forces on x-direction is ________
A.	\(\frac{∂σ_x}{∂x} + \frac{∂τ_{yx}}{∂y} + \frac{∂τ_{zx}}{∂z} +X=0\)
B.	\(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)
C.	\(\frac{∂τ_{xz}}{∂x} +\frac{∂τ_{yz}}{∂y} +\frac{∂σ_z}{∂z} +Z=0\)
D.	\(\frac{∂σ_x}{∂x}+\frac{∂τ_{yx}}{∂y} +\frac{∂τ_{zx}}{∂z} = 0\)
Answer» B. \(\frac{∂τ_{xy}}{∂x} + \frac{∂σ_y}{∂y} +\frac{∂τ_{zy}}{∂z}+Y=0\)

14.	The normal stress component acting at the centre, in the given diagram, will be _________ to the face (A C C1 A1).
A.	increased to \((σ_y+\frac{∂σ_y}{∂y}\frac{dy}{2}) \)
B.	decreased to \((σ_y-\frac{∂σ_y}{∂y}\frac{dy}{2}) \)
C.	equal to σY
D.	equal to σz
Answer» C. equal to σY

15.	The normal stress component acting at the centre, in the given diagram, will be _________ to the face (B D D1 B1).
A.	increased to \((σ_y+\frac{∂σ_y}{∂y}\frac{dy}{2}) \)
B.	decreased to \((σ_y-\frac{∂σ_y}{∂y}\frac{dy}{2}) \)
C.	equal to σY
D.	equal to σz
Answer» B. decreased to \((σ_y-\frac{∂σ_y}{∂y}\frac{dy}{2}) \)