# Applied Mechanics and Design (Test 3)

## Gate Exam : Me Mechanical Engineering

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Applied Mechanics and Design
| Applied Mechanics and Design |
Q.1
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details:
Width of the plate w=200 mm, thickness of the plate t=5 mm, number of rivets n=3, diameter of the rivet dr = 10mm, diameter of the rivet hole dh = 11mm, allowable tensile stress of the plate σp = 200 MPa, allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the σc = 150 MPa
If the rivets are to be designed to avoid crushing failure, the maximum permissible load P in kN is

A. 7.50
B. 15.00
C. 22.50
D. 30.00
Explaination / Solution:
No Explaination.

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Q.2
A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E1 to E2 along the length of the rod, the normal stress developed at the section-SS is

A. P/A(P(E- E2)) / (A(E+ E2))
B. PE2/AE1
C. PE1/AE2
Explaination / Solution:

Stress depends on area.

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Q.3
Consider a laminar flow at zero incidence over a flat plate. The shear stress at the wall is denoted by τw. The axial positions x1 and x2 on the plate are measured from the leading edge in the direction of flow. If x2 > x1, then
A.
B.
C.
D.
Explaination / Solution:

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Q.4
Match the approaches given below to perform stated kinematics / dynamics analysis of machine
Analysis                                                 Approach
P. Continuous relative rotation              1. D’ Alembert’s principle
Q. Velocity and acceleration                 2. Grubler’s criterion
R. Mobility                                             3. Grashoff’s law
S. Dynamic-static analysis                    4. kennedy’s theorem
A. P - 1, Q - 2, R - 3, S - 4
B. P - 3, Q - 4, R - 2, S - 1
C. P - 2, Q - 3, R - 4, S - 1
D. P - 4, Q - 2, R - 1, S - 3
Explaination / Solution:
No Explaination.

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Q.5
For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?
A. Metacentre should be below centre of gravity
B. Metacentre should be above centre of gravity
C. Metacentre and centre of gravity must lie on the same horizontal line
D. Metacentre and centre of gravity must lie on the same vertical line
Explaination / Solution:
No Explaination.

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Q.6
The principal stresses at a point inside a solid object are σ1 = 100 MPa, σ2 = 100 MPa and σ3 = 0MPa. The yield strength of the material is 200 MPa. The factor of safety calculated using Tresca (maximum shear stress) theory is nT and the factor of safety calculated using von Mises (maximum distortional energy) theory is nV. Which one of the following relations is TRUE?
A. n= (√3/2)nV
B. n= (√3)nV
C. n= nV
D. nV = (√3)nT
Explaination / Solution:
No Explaination.

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Q.7
A long thin walled cylindrical shell, closed at both ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is
A. 0.5
B. 1.0
C. 2.0
D. 4.0
Explaination / Solution:

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Q.8
A pinion with radius r1, and inertia I1 is driving a gear with radius r2 and inertia I2. Torque τ1 is applied on pinion. The following are free body diagrams of pinion and gear showing important forces (F1 and F2) of interaction. Which of the following relations hold true?

A.
B.
C.
D.
Explaination / Solution:

F1 = F2 [Vertical equilibrium]
For Gear 1 For Gear 2

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Q.9
For an opaque surface, the absorptivity (α), transmissivity (τ) and reflectivity (ρ) are related by the equation:
A. α + ρ = τ
B. α + ρ = 1
C. α + ρ + τ = 0
D. α + ρ = 0
Explaination / Solution:
No Explaination.

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Q.10
A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to a height of 25 mm. The percentage change in diameter is
A. 0
B. 2.07
C. 20.7
D. 41.4