# Applied Mechanics and Design (Test 2)

## Gate Exam : Me Mechanical Engineering

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Applied Mechanics and Design
| Applied Mechanics and Design |
Q.1
A torque T is applied at the free end of a stepped rod of circular cross-sections as shown in the figure. The shear modulus of the material of the rod is G. The expression for d to produce an angular twist θ at the free end is

A.

(32TL/πθG)1/4

B.

(18TL/πθG)1/4

C.

(16TL/πθG)1/4

D.

(2TL/πθG)1/4

Explaination / Solution:

Angular twist at the free end

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Q.2
A 1 kg block is resting on a surface with coefficient of friction µ = 0.1. A force of 0.8N is applied to the block as shown in figure. The friction force is

A. 0
B. 0.8N
C. 0.98N
D. 1.2N
Explaination / Solution:

Limiting friction force between the block and the surface is 0.98N. But the applied force is 0.8N which is less than the limiting friction force. Therefore the friction force for the given case is 0.8N.

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Q.3
A cantilever beam of length L and flexural modulus EI is subjected to a point load P at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear)
A. P2L3/6EI
B. P2L3/3EI
C. PL3/3EI
D. PL3/6EI
Explaination / Solution:

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Q.4
A frame of two arms of equal length L is shown in the below figure. The flexural rigidity of each arm of the frame is EI. The vertical deflection at the point of application of load P is

A. PL3/3EI
B. 2PL3/3EI
C. PL3/EI
D. 4PL3/3EI
Explaination / Solution:
No Explaination.

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Q.5
Tooth interference in an external involute spur gear pair can be reduced by
A. decreasing center distance between gear pair
B. decreasing module
C. decreasing pressure angle
D. increasing number of gear teeth
Explaination / Solution:
No Explaination.

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Q.6
A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1m, the magnitude of the absolute acceleration of the block at location A in  m/ S2 is

A. 3
B. 4
C. 5
D. 6
Explaination / Solution:

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Q.7
Two pipes of inner diameter 100 mm and outer diameter 110 mm each are joined by flash-butt welding using 30 V power supply. At the interference, 1 mm of material melts from each pipe which has a resistance of 42.4Ω. If the unit melt energy is 64.4 MJm-3, then time required for welding (in s) is
A. 1
B. 5
C. 10
D. 20
Explaination / Solution:
No Explaination.

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Q.8
For the truss shown in figure, the magnitude of the force in member PR and the support reaction at R are respectively

A. 122.47 kN and 50 kN
B. 70.71 kN and 100 kN
C. 70.71 kN and 50 kN
D. 81.65 kN and 100 kN
Explaination / Solution:

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Q.9
The following are the data for two crossed helical gears used for speed reduction:
Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle 30°
Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5°
If the input speed is 1440 rpm, the output speed in rpm is
A. 1200
B. 875
C. 900
D. 720
Explaination / Solution:

For helical gears

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Q.10
A stepped steel shaft shown below is subjected to 10 Nm torque. If the modulus of rigidity is 80 GPa, the strain energy in the shaft in N-mm is

A. 4.12
B. 3.46
C. 1.73
D. 0.86