Explore topic-wise MCQs in Soil Mechanics.

This section includes 12 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.

When the ground is horizontal, \(α=\frac{π}{2}\) in constant K. What will be the radial stress σr due to inclined line load at the horizontal ground surface?

A. \(σ_r=\frac{Q cos⁡θ}{r}\)
B. \(σ_r=\frac{2Q cos(θ-β)}{πr}\)
C. \(σ_r=\frac{Q sin⁡θ}{r}\)
D. \(σ_r=\frac{2Q sin⁡θ}{r}\)
Answer» C. \(σ_r=\frac{Q sin⁡θ}{r}\)
Discussion
2.

The radial stress component σr due to inclined line load of intensity Q per unit length is given by ___________

A. \(σ_r=\frac{2Q}{r}(\frac{cosβcosθ}{2α+sin2α})\)
B. \(σ_r=\frac{2Q}{r} (\frac{cosβcosθ}{2α+sin2α}+\frac{sinβsinθ}{2α-sin2α})\)
C. \(σ_r=\frac{Q}{r} (\frac{cosβcosθ}{2α+sin2α}+\frac{sinβsinθ}{2α-sin2α})\)
D. \(σ_r=\frac{2Q}{r}(\frac{sinβsinθ}{2α-sin2α})\)
Answer» C. \(σ_r=\frac{Q}{r} (\frac{cosβcosθ}{2α+sin2α}+\frac{sinβsinθ}{2α-sin2α})\)
Discussion
3.

The shear stress component in xz-plane in Cartesian coordinates for horizontal line load is ___________

A. \(τ_{xz}=\frac{2Q}{xzsinθcos⁡θ} \)
B. \(τ_{xz}=\frac{2Qxz^2}{π(x^2+z^2)^2} \)
C. \(τ_{xz}=\frac{2Qx^3}{π(x^2+z^2)^2} \)
D. \(τ_{xz}=\frac{2Qx^2 z}{π(x^2+z^2)^2} \)
Answer» E.
Discussion
4.

The stress component in x-direction on a horizontal plane in Cartesian coordinates for horizontal line load is ___________

A. \(σ_x=\frac{2Q}{xzsinθcos⁡θ} \)
B. \(σ_x=\frac{2Qxz^2}{π(x^2+z^2)^2} \)
C. \(σ_x=\frac{2Qx^3}{π(x^2+z^2)^2} \)
D. \(σ_x=\frac{2Qx^2 z}{π(x^2+z^2)^2} \)
Answer» D. \(σ_x=\frac{2Qx^2 z}{π(x^2+z^2)^2} \)
Discussion
5.

The relation between the shear stress component in xz-plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

A. τxz=σr tan2⁡θ
B. τxz=σr cosec2⁡θ
C. τxz=σr sinθcos⁡θ
D. τxz=σr sin2⁡θ
Answer» D. τxz=σr sin2⁡θ
Discussion
6.

The relation between the stress component in z-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

A. σz=σr cos2⁡θ
B. σz=σr cosec2⁡θ
C. σz=σr cos⁡θ
D. σz=σr sin2⁡θ
Answer» B. σz=σr cosec2⁡θ
Discussion
7.

The relation between the stress component in x-direction on a horizontal plane in Cartesian coordinates and polar coordinates for vertical line load is ___________

A. σx=σr tan2⁡θ
B. σx=σr cosec2⁡θ
C. σx=σr cos⁡θ
D. σx=σr sin2⁡θ
Answer» E.
Discussion
8.

When the ground is horizontal, \(α=\frac{π}{2}\) in constant K. What will be the radial stress σr due to vertical line load?

A. \(σ_r=\frac{Q cos⁡θ}{r}\)
B. \(σ_r=\frac{2Q cos⁡θ}{πr}\)
C. \(σ_r=\frac{Q sin⁡θ}{r}\)
D. \(σ_r=\frac{2Q sin⁡θ}{r}\)
Answer» C. \(σ_r=\frac{Q sin⁡θ}{r}\)
Discussion
9.

In simple radial distribution, if \(σ_r=K \frac{Q cos⁡θ}{r},\) then the value of K is ________

A. K=\(\frac{2}{2α+sin2α}\)
B. K=2α+sinα
C. K=2α-sinα
D. K=sinα
Answer» B. K=2α+sinα
Discussion
10.

The compatibility equation in terms of stress components in polar coordinates are given by ____________

A. \((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r+σ_θ )=0\)
B. \((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_θ )=0\)
C. \((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r )=0\)
D. \((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_r+σ_θ )=1\)
Answer» B. \((\frac{∂^2}{∂r^2} +\frac{1}{r} \frac{∂}{∂r}+\frac{1}{r^2} \frac{∂^2}{∂θ^2} )(σ_θ )=0\)
Discussion
11.

The equilibrium equation in polar coordinates is given by _____________

A. \(\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)
B. \(\frac{∂σ_r}{∂r}+\frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)
C. \(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}+\frac{σ_r-σ_θ}{r}=0\)
D. \(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}=0\)
Answer» D. \(\frac{∂σ_r}{∂r}+\frac{1}{r} \frac{∂τ_{rθ}}{∂θ}=0\)
Discussion
12.

In simple radial distribution, the three stress components σr, σθ and τrθ are given by ___________

A. \(σ_r=K \frac{Q cos⁡θ}{r}, σ_θ=0 \,and\, τ_{rθ}=0 \)
B. σr=KQ, σθ=0 and τrθ=0
C. \(σ_r=\frac{Q cos⁡θ}{r}, σ_θ=0 \,and\, τ_{rθ}=0\)
D. σr=0, σθ=0 and τrθ= 0
Answer» B. σr=KQ, σθ=0 and τrθ=0
Discussion