Applied Mechanics and Design - Online Test

Q1. 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
Answer : Option B
Explaination / Solution:

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

Q2. 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 


Answer : Option B
Explaination / Solution:

Angular twist at the free end


Q3. Two identical ball bearings P and Q are operating at loads 30kN and 45kN respectively. The ratio of the life of bearing P to the life of bearing Q is
Answer : Option B
Explaination / Solution:



Q4. For the four-bar linkage shown in the figure, the angular velocity of link AB is 1 rad/s. the length of link CD is 1.5 times the length of link AB. In the configuration shown, the angular velocity of link CD in rad/s is

Answer : Option D
Explaination / Solution:

For the given configuration 


Q5. A stone with mass of 0.1kg is catapulted as shown in the figure. The total force Fx (in N) exerted by the rubber band as a function of distance x (in m) is given by F = 300x2. If the stone is displaced by 0.1m from the un-stretched position (x=0) of the rubber band, the energy stored in the rubber band is 

Answer : Option B
Explaination / Solution:

Energy stored in the bar = W.D. by the stone 


Q6. A mass of 1kg is attached to two identical springs each with stiffness k = 20kN/m as shown in the figure. Under frictionless condition, the natural frequency of the system in Hz is close to 

Answer : Option A
Explaination / Solution:

Natural frequency of the system


Q7. The shear strength of a sheet metal is 300MPa. The blanking force required to produce a blank of 100mm diameter from a 1.5 mm thick sheet is close to
Answer : Option C
Explaination / Solution:

 Blanking force = τ . As  = 300 × πdt = 300 × π × 100 × 1.5 = 141 kN

Q8. 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 


Answer : Option C
Explaination / Solution:
No Explaination.


Q9. 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 

Answer : Option B
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.

Q10. A single–point cutting tool with 12o rake angle is used to machine a steel work– piece. The depth of cut, i.e. uncut thickness is 0.81mm. The chip thickness under orthogonal machining condition is 1.8mm. The shear angle is approximately 
Answer : Option B
Explaination / Solution:

Relation between shear angle (φ), chip thickness ratio (r) and rake angle (α) is given by