# ME GATE 2013 (Test 5)

Tag: me gate 2013
Q.1
After several defeats in wars, Robert Bruce went in exile and wanted to commit suicide. Just before committing suicide, he came across a spider attempting tirelessly to have its net. Time and again the spider failed but that did not deter it to refrain from making attempts. Such attempts by the spider made Bruce curious. Thus, Bruce started observing the near-impossible goal of the spider to have the net. Ultimately, the spider succeeded in having its net despite several failures. Such act of the spider encouraged Bruce not to commit suicide. And then, Bruce went back again and won many a battle, and the rest is history. Which one of the following assertions is best supported by the above information?
A. Failure is the pillar of success
B. Honesty is the best policy
C. Life begins and ends with adventures
D. No adversity justifies giving up hope
Explaination / Solution:
No Explaination.

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Topic: Arithmetic Tag: ME GATE 2013
Q.2
The current erection cost of a structure is Rs. 13,200. If the labour wages per day increase by 1/5 of the current wages and the working hours decrease by 1/24 of the current period, then the new cost of erection in Rs. is
A. 16,500
B. 15,180
C. 11,000
D. 10,120
Explaination / Solution:

Let ‘W’ be the labour wages, and ‘T’ be the working hours.
Now, total cost is a function of W ×T
Increase in wages = 20%
∴ Revised wages = 1.2 W
Decrease in labour time = (100/24)%
Re vised time = (1- (1/24))T = 23/24 T
Re vised Total cost = 1.2 × (23/24)WT = 1.15 WT
= 1.15 × 13200 = 15180

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Q.3
Two cutting tools are being compared for a machining operation. The tool life equations are:
Carbide tool:  VT1.6 = 3000
HSS tool:        VT0.6 = 200
Where V is the cutting speed in m/min and T is the tool life in min. The carbide toll will provide higher tool life if the cutting speed in m/min exceeds
A. 15.0
B. 39.4
C. 49.3
D. 60.0
Explaination / Solution:
No Explaination.

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Q.4
The pressure, dry bulb temperature, and relative humidity of air in a room are1bar, 30ºC and 70% respectively. If the saturated steam pressure at 30ºC is 4.25kPa, the specific humidity of the room air in kg water vapour / kg dry air is
A. 0.0083
B. 0.0101
C. 0.0191
D. 0.0232
Explaination / Solution:

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Q.5
Water is coming out from a tap and falls vertically downwards. At the tap opening, the stream diameter is 20mm with uniform velocity of 2 m/s. Acceleration due to gravity is 9.81m / s2. Assuming steady, inviscid flow, constant atmospheric pressure everywhere and neglecting curvature and surface tension effects, the diameter is mm of the stream 0.5m below the tap is approximately
A. 10
B. 15
C. 20
D. 25
Explaination / Solution:
No Explaination.

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Q.6
A hinged gate of length 5 m, inclined at 30° with the horizontal and with water mass on its left, is shown in figure below. Density of water is 1000 kg / m2. The minimum mass of the gate in kg per unit width (perpendicular to the plane of paper), required to keep it closed is

A. 5000
B. 6600
C. 7546
D. 9623
Explaination / Solution:
No Explaination.

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Q.7
In a simple Brayton cycle, the pressure ration is 8 and temperatures at the entrance of compressor and turbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficiencies equal to 0.8. For the gas, assume a constant value of cp (specific heat at constant pressure) equal to 1 kJ/kgK and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.
The thermal efficiency of the cycle in percentage (%) is
A. 24.8
B. 38.6
C. 44.8
D. 53.1
Explaination / Solution:
No Explaination.

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Q.8
A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1m, the magnitude of the absolute acceleration of the block at location A in  m/ S2 is

A. 3
B. 4
C. 5
D. 6
Explaination / Solution:

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Q.9
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

A. zero
B. W/4
C. W/2
D. W
Explaination / Solution:
No Explaination.

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Q.10
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details:
Width of the plate w=200 mm, thickness of the plate t=5 mm, number of rivets n=3, diameter of the rivet dr = 10mm, diameter of the rivet hole dh = 11mm, allowable tensile stress of the plate σp = 200 MPa, allowable shear stress of the rivet σs = 100 MPa and allowable bearing stress of the σc = 150 MPa
If the plates are to be designed to avoid tearing failure, the maximum permissible load P in kN is
A. 83
B. 125
C. 167
D. 501