Mechanical Engineering Gate Yearwise
Mechanical Engineering GATE 2023 Questions with Answer
Ques 53 Mechanics of Materials
The figure shows a thin-walled open-top cylindrical vessel of radius r and wall thickness t. The vessel is held along the brim and contains a constant-density liquid to height h from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls. Which one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress (σ1) and circumferential wall stress (σ2) on y?
Ques 54 Mechanics of Materials
Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible.
The bars are held between rigid supports as shown in the figure and the temperature is raised by ΔT. Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by σ1 and σ2, respectively.
Which of the statement(s) given is/are CORRECT?
Ques 55 Theory of Machines
Two meshing spur gears 1 and 2 with diametral pitch of 8 teeth per mm and an angular velocity ratio |ω1|/|ω2|=1/4 have their centers 30 mm apart. The number of teeth on the driver (gear 1) is _______.
(Answer in integer)
20 is the correct answer.
Ques 56 Theory of Machines
The figure shows a block of mass m=20 kg attached to a pair of identical linear springs, each having a spring constant k=1000 N/m. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is _______ seconds.
(Rounded off to two decimal places)
Take =3.14.
9.42 is the correct answer.
Ques 57 Theory of Machines
The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over an angle α=270 degrees. The coefficient of friction between the belt and the pulley is 0.3. The influence of centrifugal forces on the belt is negligible.
During braking, the ratio of the tensions T1 to T2 in the belt is equal to _______.
(Rounded off to two decimal places)
Take π=3.14
4.11 is the correct answer.
Ques 58 Theory of Machines
The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity ω1. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.
What is the angular velocity ω2 of the bar PQ?
Ques 59 Thermodynamics
Consider a mixture of two ideal gases, X and Y, with molar masses M'X = 10 kg/kmol and M'Y = 20 kg/kmol, respectively, in a container. The total pressure in the container is 100 kPa, the total volume of the container is 10 m3 and the temperature of the contents of the container is 300 K. If the mass of gas-X in the container is 2 kg, then the mass of gas-Y in the container is ____ kg.
(Rounded off to one decimal place)
Assume that the universal gas constant is 8314 J kmol-1K-1.
1.6 is the correct answer.
Ques 60 Thermodynamics
A heat engine extracts heat (QH) from a thermal reservoir at a temperature of 1000 K and rejects heat (QL) to a thermal reservoir at a temperature of 100 K, while producing work (W). Which one of the combinations of [QH QI and W] given is allowed?
Ques 61 Thermodynamics
Which one of the following statements is FALSE?
Ques 62 Thermodynamics
Consider a fully adiabatic piston-cylinder arrangement as shown in the figure. The piston is massless and cross-sectional area of the cylinder is A. The fluid inside the cylinder is air (considered as a perfect gas), with γ being the ratio of the specific heat at constant pressure to the specific heat at constant volume for air. The piston is initially located at a position L1. The initial pressure of the air inside the cylinder is P1>>P0, where P0 is the atmospheric pressure. The stop S1 is instantaneously removed and the piston moves to the position L2, where the equilibrium pressure of air inside the cylinder is P2>>P0.
What is the work done by the piston on the atmosphere during this process?
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