Mechanical Engineering Gate Yearwise
Mechanical Engineering Gate 2022 Set-1 Questions with Answer
Ques 53 GATE 2022 SET-1
An L-shaped elastic member ABC with slender arms AB and BC of uniform cross section is clamped at end A and connected to a pin at end C. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end C is subjected to a horizontal force 𝑃 and all the deflections are in the plane of the figure. Given the length AB is 4𝑎 and length BC is 𝑎, the magnitude and direction of the normal force on the pin from the slot, respectively, are
Ques 54 GATE 2022 SET-1
tructure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. AE is a single member that contains pin C. Likewise, BE is a single member that contains pin D. Members GI and FH are overlapping rigid members. The magnitude of the force carried by member CI is ________ kN (in integer).
Ques 55 GATE 2022 SET-1
Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectively. A vertical force F acts on the pin R. When the included angle θ < 90°, the rods remain in static equilibrium due to Coulomb friction between the rods and ground at locations P and Q. At θ = 90°, impending slip occurs simultaneously at points P and Q. Then the ratio of the coefficient of friction at Q to that at P (µQ /µP) is _________ (round off to two decimal places).
Ques 56 GATE 2022 SET-1
A thin-walled cylindrical pressure vessel has mean wall thickness of t and nominal radius of r. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became t̅. The corresponding change in the wall thickness of the cylindrical portion, i.e., 100 × (t̅ − t)/t, is ________% (round off to 3 decimal places).
Ques 57 GATE 2022 SET-1
A uniform light slender beam AB of section modulus EI is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight W. If the maximum value of W to avoid buckling of the beam AB is obtained as βπ2EI, then the value of β is?
Ques 58 GATE 2022 SET-1
A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB ⊥ CE and FD ⊥ CE. The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is
Ques 59 GATE 2022 SET-1
A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and planet (gear 2) are external, and the ring gear (gear 3) is internal. Gear 1, gear 3 and arm OP are pivoted to the ground at O. Gear 2 is carried on the arm OP via the pivot joint at P, and is in mesh with the other two gears. Gear 2 has 20 teeth and gear 3 has 80 teeth. If gear 1 is kept fixed at 0 rpm and gear 3 rotates at 900 rpm counter clockwise (ccw), the magnitude of angular velocity of arm OP is __________rpm (in integer)
Ques 60 GATE 2022 SET-1
The Clausius inequality holds good for?
Ques 61 GATE 2022 SET-1
A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m³ to a final volume of 2.5 m³. The polytropic index is given by n = 1.2. The absolute value of the work done during the process is _______ kJ (round off to 2 decimal places).
Ques 62 GATE 2022 SET-1
In a steam power plant based on Rankine cycle, steam is initially expanded in a high-pressure turbine. The steam is then reheated in a reheater and finally expanded in a low-pressure turbine. The expansion work in the high-pressure turbine is 400 kJ/kg and in the low-pressure turbine is 850 kJ/kg, whereas the pump work is 15 kJ/kg. If the cycle efficiency is 32%, the heat rejected in the condenser is ________ kJ/kg (round off to 2 decimal places).
Ques 63 GATE 2022 SET-1
An engine running on an air standard Otto cycle has a displacement volume 250 cm³ and a clearance volume 35.7 cm³. The pressure and temperature at the beginning of the compression process are 100 kPa and 300 K, respectively. Heat transfer during constant-volume heat addition process is 800 kJ/kg.. The specific heat at constant volume is 0.718 kJ/kg.K and the ratio of specific heats at constant pressure and constant volume is 1.4. Assume the specific heats to remain constant during the cycle. The maximum pressure in the cycle is ______ kPa (round off to the nearest integer).
Ques 64 GATE 2022 SET-1
A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius 𝑟 and outer radius 𝑅 are such that 𝑟 =𝑅2/2, and the acceleration due to gravity is 𝑔. If the time period of small amplitude simple harmonic motion is given by 𝑇=𝛽𝜋√(𝑅/𝑔), where 𝜋 is the ratio of circumference to diameter of a circle, then 𝛽= ________ (round off to 2 decimal places).
Ques 65 GATE 2022 SET-1
Consider a forced single degree-of-freedom system governed by
mẍ(t) + 2ζωẋ(t) + ω2x(t) = ω2 cos(ωt),
where ζ and ω are the damping ratio and undamped natural frequency of the system, respectively, while ωf is the forcing frequency. The amplitude of the forced steady state response of this system is given by [ (1 - r2)2 + (2ζr)2 ]-1/2, where r = ωf/ω. The peak amplitude of this response occurs at a frequency ωf = ω√(1 - 2ζ2). If ωd denotes the damped natural frequency of this system, which one of the following options is true?
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