Applied Mechanics and Design - Online Test

Q1. A triangular–shaped cantilever beam of uniform–thickness is shown in the figure. The Young’s modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam. 

The area moment of inertia about the neutral axis of a cross-section at a distance x measured from the free end is
Answer : Option B
Explaination / Solution:
No Explaination.


Q2. A triangular–shaped cantilever beam of uniform–thickness is shown in the figure. The Young’s modulus of the material of the beam is E. A concentrated load P is applied at the free end of the beam. 

The maximum deflection of the beam is 
Answer : Option D
Explaination / Solution:
No Explaination.


Q3. 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)
Answer : Option A
Explaination / Solution:



Q4. 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
Answer : Option C
Explaination / Solution:



Q5.
A mass m is attached to two identical springs having spring constant k as shown in the figure. The natural frequency 𝜔 of this single degree of freedom system is

Answer : Option A
Explaination / Solution:



Q6. A steel plate, connected to a fixed channel using three identical bolts A, B and C, carries a load of 6kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt C is.

Answer : Option C
Explaination / Solution:

Primary shear = 6/3 = 2kN
Secondaryshear 1500 kN - mm

Resultantshear at 'C' = 2 + 15 = 17kN
Resultant shear = 15 + 2 = 17 kN

Q7. 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
Answer : Option B
Explaination / Solution:



Q8. The principal stresses at a point in a critical section of a machine component are σ= 60MPa, σ= 5MPa and σ= -40 MPa. For the material of the component, the tensile yield strength is σ= 200 MPa. According to the maximum shear stress theory, the factor of safety is
Answer : Option B
Explaination / Solution:



Q9. The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that r3> r1 and r4> r2, and that the areas of the cross-sections are the same. J1 and J2 are the torsional rigidities of the bars on the left and right, respectively. The ratio J2/J1 is

Answer : Option A
Explaination / Solution:

Torsional rigidity for any Shaft is given by, 
J = GIP
Or J α IP (Polar moment of Inertia) And for a hollow shaft, 


Q10. A cantilever beam having square cross-section of side a is subjected to an end load. If a is increased by 19%, the tip deflection decreases approximately by
Answer : Option D
Explaination / Solution:


From the deflection formula, for cantilever beam having point load at its free end, 

Hence, decrement in the deflection in percentage will be