ME GATE 2011 - Online Test
Q1. A cubic casting of 50mm side undergoes volumetric solidification shrinkage and
volumetric solid contraction of 4% and 6% respectively. No. riser is used.
Assume uniform cooling in all directions. The side of the cube after solidification
and contraction is
Answer : Option A
Explaination / Solution:
Volumetric solidification shrinkage and volumetric solid contraction cause
decrease in dimensions.
Volume of cube = 503 = 125000 mm3
After considering both the allowances
V = 125000 × 0.96 × 0.94 = 112800mm3
Q2. A column has a rectangular cross-section of 10mm x 20mm and a length of 1m.
The slenderness ratio of the column is close to
Answer : Option B
Explaination / Solution:
No Explaination.
Q3. The crank radius of a single–cylinder I. C. engine is 60mm and the diameter of
the cylinder is 80mm. The swept volume of the cylinder in cm3 is
Answer : Option D
Explaination / Solution:
Stroke of the cylinder l = 2r = 2 × 60 = 120mm
Swept volume = (π/4)d2 × I = (π/4) × 802 × 120 = 603 cm3
Q4. The variable cost (V) of manufacturing a product varies according to the equation
V= 4q, where q is the quantity produced. The fixed cost (F) of production of same
product reduces with q according to the equation F = 100/q. How many units
should be produced to minimize the total cost (V+F)?
Answer : Option A
Explaination / Solution:
Checking with all options in formula: (4q+100/q) i.e. (V+F). Option A gives the
minimum cost.
Q5. Match the following criteria of material failure, under biaxial stresses σ1 and σ2 and yield stress σy , with their corresponding graphic representations :
P. Maximum-normal-stress criterion L. 
Q. Maximum-distortion-energy criterion M. 
R. Maximum-shear–stress criterion N. 
Answer : Option C
Explaination / Solution:
No Explaination.
Q6. 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
Q7. A pump handling a liquid raises its pressure from 1 bar to 30 bar. Take the
density of the liquid as 990 kg /m3. The isentropic specific work done by the
pump in kJ/kg is
Answer : Option D
Explaination / Solution:
Work done by the pump = 
Q8. 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
Q9. A spherical steel ball of 12mm diameter is initially at 1000K. It is slowly cooled in
a surrounding of 300K. The heat transfer coefficient between the steel ball and
the surrounding is 5W /m2 K . The thermal conductivity of steel is 20W /mK . The
temperature difference between the centre and the surface of the steel ball is
Answer : Option D
Explaination / Solution:
Bi = hL/K = 5 ×0.002/20 = 0.0005
For the given condition the Biot number tends to zero, that means conduction
resistance is far less than convection resistance. Therefore temperature between
the centre and surface is very small.
Q10. 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:
