Mechanical Engineering Gate 2013 Set-2 Questions with Answer

Ques 40 GATE 2013 SET-2

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure. If the Young's modulus of the material varies linearly from E₁ to E₂ along the length of the rod, the normal stress developed at the section-SS is

Ques 41 GATE 2013 SET-2

The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s, respectively. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of the air stream is

Ques 42 GATE 2013 SET-2

A hinged gate of length 5 m, inclined at 30° with the horizontal and with water mass on its left, is shown in the figure. Density of water is 1000 kg/m³. The minimum mass of the gate in kg per unit width (perpendicular to the plane of paper), required to keep it closed is

Ques 43 GATE 2013 SET-2

Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is 5.67×10^-8 W/m²K⁴, the net radiation heat exchange rate in kW/m² between the two plates is

Ques 44 GATE 2013 SET-2

A simply supported beam of length L is subjected to a varying distributed load sin(3πx/L) Nm^-1, where the distance x is measured from the left support. The magnitude of the vertical reaction force in N at the left support is

Ques 45 GATE 2013 SET-2

A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of cross-section in mm² of the bar for a factor of safety of 2 is

Ques 46 GATE 2013 SET-2

A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected to an impulse force of magnitude 5 kN for 10^-4 seconds. The amplitude in mm of the resulting free vibration is

Ques 47 GATE 2013 SET-2

During the electrochemical machining (ECM) of iron (atomic weight = 56, valency = 2) at current of 1000 A with 90% current efficiency, the material removal rate was observed to be 0.26 gm/s. If Titanium (atomic weight = 48, valency = 3) is machined by the ECM process at the current of 2000 A with 90% current efficiency, the expected material removal rate in gm/s will be

Ques 48 GATE 2013 SET-2

Cylindrical pins of 25^+0.020_+0.010 mm diameter are electroplated in a shop. Thickness of the plating is 30±2.0 micron. Neglecting gage tolerances, the size of the GO gage in mm to inspect the plated components is

Ques 49 GATE 2013 SET-2

A linear programming problem is shown below.
Maximize 3x + 7y
Subject to
3x + 7y ≤ 10
4x + 6y ≤ 8
x, y ≥ 0
It has

Ques 50 GATE 2013 SET-2

In a CAD package, mirror image of a 2D point P(5,10) is to be obtained about a line which passes through the origin and makes an angle of 45° counterclockwise with the X-axis. The coordinates of the transformed point will be

Ques 51 GATE 2013 SET-2

Two cutting tools are being compared for a machining operation. The tool life equations are:
Carbide tool: VT^1.6 = 3000
HSS tool: VT^0.6 = 200
where V is the cutting speed in m/min and T is the tool life in min. The carbide tool will provide higher tool life if the cutting speed in m/min exceeds

Ques 52 GATE 2013 SET-2

A pin jointed uniform rigid rod of weight W and length L is supported horizontally by an external force F as shown in the figure below. The force F is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is