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# Quiz: Mechanical Engineering 28th April

Quiz: Mechanical Engineering
Exam: GATE
Topic: Miscellaneous

Each question carries 2 mark
Negative marking: 1/3 mark
Time: 20 Minutes

Q1. Two identical circular rods of same diameter and same length are subjected to same magnitude of axial tensile force. One of the rods is made out of mild steel having the modulus of elasticity of 206 GPa. The other rod is made out of cast iron having the modulus of elasticity of 100 GPa. Assume both the materials to be homogeneous and isotropic and the axial force causes the same amount of uniform stress in both the rods. The stresses developed are within the proportional limit of the respective materials. Which of the following observations is correct?
(a) Both rods elongate by the same amount
(b) Mild steel rod elongates more than the cast iron
(c) cast iron rod elongates more than the mild steel rod
(d) as the stresses are equal strains are also equal in both the rods

Q2. Engineering strain of a mild steel sample is recorded as 0.100%. the true strain is
(a) 0.010%
(b) 0.055%
(c) 0.099%
(d) 0.101%

Q3. Within a boundary layer for a steady incompressible flow, the Bernoulli equation
(a) holds because the flow is steady
(b) holds because the flow is incompressible
(c) holds because the flow is transitional
(d) does not hold because the flow is frictional

Q4. Consider the triangular formed by the connecting rod and the crank of an IC engine as the two sides of the triangle. If the maximum area of this triangle occurs when the crank is 75°, the ratio of connecting rod length to crank radius to
(a) 5
(b) 4
(c) 3.73
(d) 3

Q5. A thin cylinder of 100 mm internal diameter and 5 mm thickness is subjected to an internal pressure of 10 MPa and a torque of 2000 Nm. Calculate the magnitudes of the principal stresses.
(a) 109.8, 45.2
(b) 109.8, 40.2
(c) 109.8, 31
(d) 109.8, 50

Q6. Navier-Stoke’s equation represents the conservation of
(a) Energy
(b) Mass
(c) Pressure
(d) Momentum

Q7. Solidification time of a metallic alloy casting is
(a) Directly proportional to its surface area
(b) Inversely proportional to the specific heat of the cast material
(c) inversely proportional to the thermal diffusively of the mould material
(d) Inversely proportional to the pouring temp

Q8. In the laminar flow of air (P_r=0.7) over a heated plate, if δ and δ_T denote, respectively, the hydrodynamic and thermal boundary layer thicknesses, then
(a) δ=δ_T
(b) δ>δ_T
(c) δ<δ_T
(d) δ=0 but δ_T≠0

Q9. A gas turbine cycle with heat exchange and reheating improves
(a) only the thermal efficiency
(b) Only the specific power output
(c) Both thermal efficiency and specific power output
(d) Neither thermal efficiency nor specific power output

Q10. There are two points P and Q on a planar rigid body. The relative velocity between the two points
(a) should always be along PQ
(b) can be oriented along any direction
(c) should always be perpendicular to PQ
(d) should be along QP when the body undergoes pure translation

Solution

S1. Ans.(c)
Sol. Given, E_S=206 GPa ;E_I=100 GPa
Elongation in mild steel,
∆L_S=PL/(AE_s )——(1)
Elongation in cast iron,
∆L_I=PL/(AE_I )—–(2)
From diving equation (2) in equation (1), we get
(∆L_S)/(∆L_1 )=E_I/E_S
Since diameter and length of both salts are equal
∵(∆L_S)/(∆L_1 )=100/206<1

S2. Ans.(c)
Sol. Given data
Engineering strain,
∈ =0.100%=0.001
True strain = ∈ ̅=ln⁡(1+∈)
ln⁡(1+0.001)
=ln⁡(1.001)
=0.00099
=0.099%

S3. Ans.(d)
Sol. Within boundary layer, Bernoulli’s equation is not valid because due to friction, flow is rotational.
S4. Ans.(c)
Sol. Area = 1/2 AB×AOSinA
For maximum area, value of SinA should be 1

i.e. ⇒ A = 90°
now consider RH triangle, AOB
tan 75° = AB/OA = 3.73

S5. Ans.(b)
Sol. Di = 100 mm
Do = 110 mm
D = 105 mm
Thin cylinder

J=πDt[D^2/4]=π×103×3×(52.5)^2
=4545982 mm^4
=4.545×10^6 mm^4
τ_max=(T×r_max)/J
Where r_max = Do/2=55⇒(2000×10^3×55)/(4.545×10^6 )
=24.20 MPa
σ_h=σ_c=Pdi/2t=100 MPa
σ_l=50 MPa
σ_1,σ_2=150/2±√(25^2+〖24.20〗^2 )
=75±34.8
σ_1=109.8 MPa
σ_2=40.2 MPa

S6. Ans.(d)
Sol. Bernoulli’s equation – law of conservation of energy
Continuity equation – law of conservation of mass
Navier-stoke’s equation – law of conservation of momentum

S7. Ans.(c)
Sol. Thermal diffusivity: α = K/〖ρC〗_p
Solidification time increases with decreases in thermal conductivity.

S8. Ans.(c)
Sol. Prandtl number,
P_r=0.7
also P_R=δ/δ_T
∵0.7 ≠δ/δ_T
or δ=0.7 δ_T
δ<δ_T

S9. Ans.(c)
Sol. A gas turbine cycle is to add both reheat and heat exchanger in order to improve the work output as well as the efficiency.

S10. Ans.(c)
Sol. V_PQ= Relative velocity between P and Q
V_PQ = V_P-V_Q
Always perpendicular to PQ.

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