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# Quiz: Mechanical Engineering 18th June

Quiz: Mechanical Engineering
Exam: AE/JE
Topic: Miscellaneous

Each question carries 2 mark
Negative marking: 1/4 mark
Time: 10 Minutes

Q1. A copper rod 400 mm long is pulled in tension to a length of 401.2 mm by applying a tensile stress of 330 MPa. If the deformation is entirely elastic, the Young’s modulus of copper is
(a) 110 GPa
(b) 110 MPa
(c) 11 GPa
(d) 11 MPa

Q2. At a point in a body, ε_1=0.0004 and ε_2= -0.00012. If E = 2 × 105 MPa and μ = 0.3, the smallest normal stress and the largest shearing stress are
(a) 40 MPa and 40 MPa
(b) 0 MPa and 40 MPa
(c) 80 MPa and 0 MPa
(d) 0 MPa and 80 MPa

Q3. The point of contraflexure is a point where:
(a) shear force changes sign
(b) bending moment changes sign
(c) shear force is maximum
(d) bending moment is maximum

Q4. A simply supported beam of rectangular cross-section is under transverse loading. Regarding the shear stress distribution across any section, the ratio of maximum shear stress to mean shear stress is
(a) 1.5
(b) 2.5
(c) 3.5
(d) 4.5

Q5. A long column hinged at both the ends has certain critical Euler’s buckling load-carrying capacity. If the same column be fixed at both the ends (in place of hinged ends), the load-carrying capacity then increases to
(a) 4 times
(b) 3 times
(c) 2 times
(d) Nil

Q6. What is the diameter of the largest sphere in terms of lattice parameter a, which will fit the void at the centre of the cube edge of a BCC crystal?
(a) 0.134a
(b) 0.25 a
(c) 0.433a
(d) 0.5a

Q7. A constitutional diagram shows relationship among which of the following combinations in a particular alloy system?
(a) temperature and composition
(b) temperature and phases present
(c) temperature, composition and phases present
(d) temperature and pressure

Q8. Elastic limit of cast iron as compared to its ultimate breaking strength is
(a) Half
(b) Double
(c) Approximately same
(d) None of the above

Q9. Sialon ceramic is used as:
(a) Cutting tool material
(b) Creep resistant
(c) furnace linens
(d) High strength

Q10. When an alloy solidifies over a range of temperature, the resulting casting structure is
(a) Wholly equi-axed
(b) Wholly columnar
(c) Partially columnar partially equi-axed
(d) Dendritic

Solutions
S1. Ans.(a)
Sol.
E=σ/E=(330×〖10〗^6)/(1.2/400)
=110×〖10〗^5Pa = 110 GPa

S2. Ans.(b)
Sol.
ε_1=0.004
ε_2= -0.00012 ; μ=0.3
E=2×〖10〗^5 MPa
σ_1=E/((1-μ^2 ) ) (ε_1+με_2 )
σ_1=(2×〖10〗^5)/(1-0.09) [0.0004+(0.3×-0.00012)]
σ_1=80 MPa
σ_2=E/((1-μ^2 ) ) (ε_2+με_1 )
=(2×〖10〗^5)/(1-0.09) (-0.00012+0.3×0.0004)
σ_2=0
τ_max=(σ_1-σ_2)/2=(80-0)/2=40 MPa

S3. Ans.(b)
Sol. At the point of contraflexure bending moment is zero i.e Bending moment changes sign.

S4. Ans.(a)
Sol. A simply supported beam of rectangular cross-section is under transverse loading. Regarding the shear stress distribution across any section, the ratio of maximum shear stress to mean shear stress is 1.5 or 3/2.

S5. Ans.(a)
Sol. P_e=(π^2 EI_min )/(L_e^2 )
For both end fixed support L_e=L/2 for both end hinge support L_e=L
∴ P_(e both the fixed)=4 P_(eboth end hinged)

S6. Ans.(a)
Sol.

The void formed is octahedral void. The largest radius that can fit in it is
R_octahedral=(a/2-r)
but,a=4/√3 r for BCC crystal structure
⇒R=2/√3 r-r=(2/√3-1)r
R_octahedral=0.158 r
Also, r=√3/4a
⇒R_octahedral=(0.158×√3)/4 ×9a
= 0.06849a
D_octahedral=2×R_octahedral
= 0.1369 a

S7. Ans.(c)
Sol. A constitutional diagram shows relationship among temperature, composition and phases present.

S8. Ans.(b)
Sol. Cast iron is brittle and hence its elastic limit and breaking limit are approximately hence.

S9. Ans.(a)
Sol. Si Al ON : It is silicon nitride-based cutting tool materials with aluminum and oxygen additions. This tool material is tougher than alumina. Aerospace alloys and nickel-based gas turbine discs can be machined using sialon tool bit at a cutting speed of 200 -300 m/mt.

S10. Ans.(d)
Sol. Solidification of pure metals : Columnar structure
Solidification of alloys : Dendritic structure

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