GATE ME format:nat PYQs & Answers — Page 33

Questions 321–330 of 418. Imported answers require independent review unless marked reviewed.

Topic practice 418 questionsPage 33 of 42

Given the ordinary differential equation

with

and

, the value of y is ________ (correct to two decimal places).

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An explicit forward Euler method is used to numerically integrate the differential equation

using a time step of 0.1. With the initial condition

, the value of

computed by this method is __________ (correct to two decimal places).

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A thin-walled cylindrical can with rigid end caps has a mean radius R = 100 mm and a wall thickness of t = 5 mm. The can is pressurized and an additional tensile stress of 50 MPa is imposed along the axial direction as shown in the figure. Assume that the state of stress in the wall is uniform along its length. If the magnitudes of axial and circumferential components of stress in the can are equal, the pressure (in MPa) inside the can is ________ (correct to two decimal places).

Diagram for Mechanical Engineering question 37

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F(s) is the Laplace transform of the function

F(1) is ________ (correct to two decimal places).

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A bar is subjected to a combination of a steady load of 60 kN and a load fluctuating between −10 kN and 90 kN. The corrected endurance limit of the bar is 150 MPa, the yield strength of the material is 480 MPa and the ultimate strength of the material is 600 MPa. The bar cross-section is square with side a. If the factor of safety is 2, the value of a (in mm), according to the modified Goodman’s criterion, is ________ (correct to two decimal places).

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A simply supported beam of width 100 mm, height 200 mm and length 4 m is carrying a uniformly distributed load of intensity 10 kN/m. The maximum bending stress (in MPa) in the beam is __________ (correct to one decimal place).

Diagram for Mechanical Engineering question 39

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A force of 100 N is applied to the centre of a circular disc, of mass 10 kg and radius 1 m, resting on a floor as shown in the figure.

If the disc rolls without slipping on the floor, the linear acceleration (in m/s

) of the centre of the disc is ________ (correct to two decimal places).

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A machine of mass

kg is supported on two mounts, each of stiffness

kN/m. The machine is subjected to an external force (in N)

. Assuming only vertical translation motion, the magnitude of the dynamic force (in N) transmitted from each mount to the ground is _____ (correct to two decimal places).

Diagram for Mechanical Engineering question 40

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A frictionless circular piston of area

and mass 100 kg sinks into a cylindrical container of the same area filled with water of density 1000 kg/m

as shown in the figure.

The container has a hole of area

at the bottom that is open to the atmosphere. Assuming there is no leakage from the edges of the piston and considering water to be incompressible, the magnitude of the piston velocity (in m/s) at the instant shown is ______ (correct to three decimal places).

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A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45° and a force of 40 N is acting towards the left on the slider. The length of the crank is 30 mm and the connecting rod is 70 mm. Ignoring the effect of gravity, friction and inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is __________ (correct to two decimal places).

Diagram for Mechanical Engineering question 41

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GATE ME format:nat PYQs

Question 36

Question 37

Question 37

Question 38

Question 38

Question 39

Question 39

Question 40

Question 40

Question 41