Mechanical Engineering
GATE ME topic:mechanical-engineering PYQs
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Questions 731–740 of 1040. Imported answers require independent review unless marked reviewed.
Question 31
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The rotor of a turbojet engine of an aircraft has a mass 180 kg and polar moment of inertia 10 kg m² about the rotor axis. The rotor rotates at a constant speed of 1100 rad/s in the clockwise direction when viewed from the front of the aircraft. The aircraft while flying at a speed of 800 km per hour takes a turn with a radius of 1.5 km to the left. The gyroscopic moment exerted by the rotor on the aircraft structure and the direction of motion of the nose when the aircraft turns, are
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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 
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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
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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 
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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;
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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
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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
is
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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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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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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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