Mechanical Engineering Gate 2013 Set-1 Questions with Answer

Ques 40 GATE 2013 SET-1

A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-rocker) mechanism is

Ques 41 GATE 2013 SET-1

Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:

Ques 42 GATE 2013 SET-1

Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is 20 mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81 m/s². Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, the diameter in mm of the stream 0.5 m below the tap is approximately

Ques 43 GATE 2013 SET-1

A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is suddenly removed from the furnace and cooled in ambient air at 30°C, with convective heat transfer coefficient h = 20 W/m²K. The thermo-physical properties of steel are: density ρ=7800 kg/m³, conductivity k=40 W/mK and specific heat c=600 J/kgK. The time required in seconds to cool the steel ball in air from 1030°C to 430°C is

Ques 44 GATE 2013 SET-1

A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg-m² is

Ques 45 GATE 2013 SET-1

A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively. Gears Q and R are mounted on the same shaft as shown in the figure. The diameter of the gear Q is twice that of the gear R. If the module of the gear R is 2 mm, the center distance in mm between gears P and S is

Ques 46 GATE 2013 SET-1

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

Ques 47 GATE 2013 SET-1

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 48 GATE 2013 SET-1

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 49 GATE 2013 SET-1

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-1

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 51 GATE 2013 SET-1

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 52 GATE 2013 SET-1

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