Topic: Applied Mechanics and Design (Test 1)

Topic: Applied Mechanics and Design
Q.1
A thin cylinder of inner radius 500mm and thickness 10mm is subjected to an internal pressure of 5MPa. The average circumferential (hoop) stress in MPa is
A. 100
B. 250
C. 500
D. 1000
Explaination / Solution:

Given Data: p = 5MPa; d = 1000mm; t = 10mm
Hoop stress = pd/2t = 250MPa

Workspace
Report
Q.2
A disc of mass m is attached to a spring of stiffness k as shown in the figure. The disc rolls without slipping on a horizontal surface. The natural frequency of vibration of the system is A. B. C. D. Explaination / Solution:
No Explaination.

Workspace
Report
Q.3
A solid circular shaft of diameter d is subjected to a combined bending moment M and torque, T. The material property to be used for designing the shaft using the relation A. ultimate tensile strength (Su)
B. tensile yield strength (Sv
C. torsional yield strength (Ssy)
D. endurance strength (Se)
Explaination / Solution:
No Explaination.

Workspace
Report
Q.4
A rod of length 20mm is stretched to make a rod of length 40 mm. Subsequently, it is compressed to make a rod of final length 10mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is
A. –0.5
B. –0.69
C. –0.75
D. –1.0
Explaination / Solution: Workspace
Report
Q.5
The natural frequency of a spring-mass system on earth is ωn. The natural frequency of this system on the moon (gmoon = gearth/ 6) is
A. ωn
B. 0.408ωn
C. 0.204ωn
D. 0.167ωn
Explaination / Solution:
No Explaination.

Workspace
Report
Q.6
A solid disc with radius a is connected to a spring at a point d above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is M and the spring constant is K. The polar moment of inertia for the disc about its center is j = Ma2/2 The natural frequency of this system in rad/s is given by
A. B. C. D. Explaination / Solution:
No Explaination.

Workspace
Report
Q.7
For the configuration shown, the angular velocity of link AB is 10 rad/s counterclockwise. The magnitude of the relative sliding velocity (in ms-1) of slider B with respect to rigid link CD is A. 0
B. 0.86
C. 1.25
D. 2.5
Explaination / Solution:
No Explaination.

Workspace
Report
Q.8
A machine element is subjected to the following bi-axial state of stress; σx = 80 MPa; σy = 20 MPa; τxy = 40MPa. If the shear strength of the material is 100 MPa, the factor of safety as per Tresca‟s maximum shear stress theory is
A. 1.0
B. 2.0
C. 2.5
D. 3.3
Explaination / Solution: Workspace
Report
Q.9
A solid disc of radius r rolls without slipping on a horizontal floor with angular velocity ω and angular acceleration α. The magnitude of the acceleration of the point of contact on the disc is
A. Zero
B.
C. D. 2
Explaination / Solution:

Tangential acceleration will be zero, radial acceleration will exist.
Hence, Total acceleration = rω2

Workspace
Report
Q.10
The threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of the bolt B and the mean diameter of bolt A is 12mm, the mean diameter of bolt B in mm is
A. 16
B. 24
C. 36
D. 48 