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# NHPC JE’21 ME: Daily Practices Quiz. 18-Oct-2021

Quiz: Mechanical Engineering
Exam: NHPC JE
Topic: SOM

Each question carries 1 mark
Negative marking: 1/4 mark
Time: 6 Minutes

Q1. The elongation in a bar of circular cross-section, having a length L subjected to a tensile load P and tapering uniformly from a diameter d_1 at one end to a diameter d_2 at the other end, is given by
(a) PL/(4Ed_1 d_2 )
(b) πPL/(Ed_1 d_2 )
(c) πPL/(4Ed_1 d_2 )
(d) 4PL/(πEd_1 d_2 )

Q2. A cylindrical rod which has cross-sectional area 200 ×10^(-6) m² is subjected to a tensile force. Based on the Tresca criterion, if the uniaxial yield stress of the material is 100 MPa, the failure load is
(a) 10 KN
(b) 20 KN
(c) 100 KN
(d) 200 KN

Q3. The maximum distortion energy theory is postulated by?
(a) Tresca
(b) Rankine
(c) St. Venant
(d) Mises-Henky

Q4. Principal planes are planes of
(a) Maximum shear stress
(b) Zero shear stress
(c) Shear stress having a magnitude of 50% of maximum normal stress
(d) will be maximum

Q5. Maximum shear strain occurs on a plane which are
(a) Principal planes
(b) Inclined at 45° with principal planes
(c) 90° with principal planes
(d) All of above

Q6. Shear span is defined as the zone where:
(a) bending moment is zero
(b) shear force is zero
(c) shear force is constant
(d) bending moment is constant

### Solutions

S1. Ans.(d)
Sol. The elongation of circular cross-section tapering uniformly from a diameter d_1 at one end to a diameter d_2 at the other end subjected to tensile load P is

δL=4PL/(πd_1 d_2 E)
S2. Ans.(b)
Sol. We know that by Tresca Theory
τ_max=(σ_1-σ_2)/2 =σ_y/2
Therefore σ_1=σ_y (σ_1=force×area)
Force = 200 × 10^6×100×10^(-6) = 20kN

S3. Ans.(d)
Sol. Maximum shear stress theory is given by Tresca
Maximum principal stress theory is given by Rankine
Maximum principal strain theory is given by St. Venant
Maximum shear strain energy theory is given by Mises – Henky

S4. Ans.(b)
Sol. Infinite plane’s passes through a single point. Out of infinite plane’s three planes are mutually perpendicular to each other and having zero shear stress, that planes are called principal plane.

S5. Ans.(b)
Sol. Maximum shear strain occur on 45° with the principal planes.

S6. Ans.(c)
Sol. Shear span is the distance from the point of application of concentrated force to its respective reaction force. throughout shear span the shear force is constant.
“Shear span is defined as the zone where shear force is constant.”

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