GATE ME format:mcq PYQs & Answers — Page 45

Questions 441–450 of 599. Imported answers require independent review unless marked reviewed.

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is

, Young’s modulus

, and area moment of inertia

, the magnitude of the maximum deflection is

Diagram for Mechanical Engineering question 31

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The wall of a constant diameter pipe of length 1 m is heated uniformly with flux

by wrapping a heater coil around it. The flow at the inlet to the pipe is hydrodynamically fully developed. The fluid is incompressible and the flow is assumed to be laminar and steady all through the pipe. The bulk temperature of the fluid is equal to 0 °C at the inlet and 50 °C at the exit. The wall temperatures are measured at three locations, P, Q and R, as shown in the figure. The flow thermally develops after some distance from the inlet. The following measurements are made:

Point	P	Q	R
Wall Temp (°C)	50	80	90

Among the locations P, Q and R, the flow is thermally developed at

Your answerChoose one option.

P, Q and R

P and Q only

Q and R only

R only

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A slender uniform rigid bar of mass

is hinged at O and supported by two springs, with stiffnesses

and

, and a damper with damping coefficient

, as shown in the figure. For the system to be critically damped, the ratio

should be

Diagram for Mechanical Engineering question 32

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A gas is heated in a duct as it flows over a resistance heater. Consider a 101 kW electric heating system. The gas enters the heating section of the duct at 100 kPa and 27 °C with a volume flow rate of 15 m³/s. If heat is lost from the gas in the duct to the surroundings at a rate of 51 kW, the exit temperature of the gas is

(Assume constant pressure, ideal gas, negligible change in kinetic and potential energies and constant specific heat,

kJ/kg·K;

kJ/kg·K.)

Your answerChoose one option.

32 °C

37 °C

53 °C

76 °C

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The figure shows a heat engine (HE) working between two reservoirs. The amount of heat (

) rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output (

) of the heat engine. If temperatures,

, then the relation between the efficiency (

) of the heat engine and the coefficient of performance (COP) of the heat pump is

Diagram for Mechanical Engineering question 33

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A plane-strain compression (forging) of a block is shown in the figure. The strain in the z-direction is zero. The yield strength (

) in uniaxial tension/compression of the material of the block is 300 MPa and it follows the Tresca (maximum shear stress) criterion. Assume that the entire block has started yielding. At a point where

MPa (compressive) and

, the stress component

Diagram for Mechanical Engineering question 34

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340 MPa (compressive)

340 MPa (tensile)

260 MPa (compressive)

260 MPa (tensile)

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The binary phase diagram of metals P and Q is shown in the figure.

An alloy X containing 60% P and 40% Q (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in weight percent) at 1250 °C, respectively, will be

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77.8% and 22.2%

22.2% and 77.8%

68.0% and 32.0%

32.0% and 68.0%

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In orthogonal turning of a cylindrical tube of wall thickness 5 mm, the axial and the tangential cutting forces were measured as 1259 N and 1601 N, respectively. The measured chip thickness after machining was found to be 0.3 mm. The rake angle was 10° and the axial feed was 100 mm/min. The rotational speed of the spindle was 1000 rpm. Assuming the material to be perfectly plastic and Merchant’s first solution, the shear strength of the material is closest to

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722 MPa

920 MPa

200 MPa

875 MPa

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The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship “X < Y, Z” means that X is predecessor of activities Y and Z. The time to complete the activities along the critical path is ______ weeks.

Activity	Duration (Weeks)	Precedence Relationship
A	5	A < B, C, D
B	7	B < E, F, G
C	10	C < I
D	6	D < G
E	3	E < H
F	9	F < I
G	7	G < I
H	4	H < I
I	2	---

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A circular shaft having diameter

mm is manufactured by turning process. A 50 μm thick coating of TiN is deposited on the shaft. Allowed variation in TiN film thickness is ± 5 μm. The minimum hole diameter (in mm) to just provide clearance fit is

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65.01

65.12

64.95

65.10

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GATE ME format:mcq PYQs

Question 31

Question 32

Question 32

Question 33

Question 33

Question 34

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Question 35

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Question 36