GATE ME branch:me PYQs & Answers — Page 24

Questions 231–240 of 1040. Imported answers require independent review unless marked reviewed.

Which one of the options given is the inverse Laplace transform of

denotes the unit-step function.

Your answerChoose one option.

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A spherical ball weighing 2 kg is dropped from a height of 4.9 m onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in kg m/s) just after impact?

Take the acceleration due to gravity to be

m/s

. Options have been rounded off to one decimal place.

Diagram for Mechanical Engineering question 37

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The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity

. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.

What is the angular velocity

of the bar PQ?

Diagram for Mechanical Engineering question 38

Your answerChoose one option.

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A beam of length

is loaded in the

-plane by a uniformly distributed load, and by a concentrated tip load parallel to the

-axis, as shown in the figure. The resulting bending moment distributions about the

and the

axes are denoted by

and

, respectively.

Which one of the options given depicts qualitatively CORRECT variations of

and

along the length of the beam?

Diagram for Mechanical Engineering question 39

Your answerChoose one option.

Diagram for Mechanical Engineering question 39 (figure 2)

Diagram for Mechanical Engineering question 39 (figure 3)

Diagram for Mechanical Engineering question 39 (figure 4)

Diagram for Mechanical Engineering question 39 (figure 5)

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The figure shows a thin-walled open-top cylindrical vessel of radius

and wall thickness

. The vessel is held along the brim and contains a constant-density liquid to height

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 (

) and circumferential wall stress (

) on

Diagram for Mechanical Engineering question 40

Your answerChoose one option.

Diagram for Mechanical Engineering question 40 (figure 2)

Diagram for Mechanical Engineering question 40 (figure 3)

Diagram for Mechanical Engineering question 40 (figure 4)

Diagram for Mechanical Engineering question 40 (figure 5)

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Which one of the following statements is FALSE?

Your answerChoose one option.

For an ideal gas, the enthalpy is independent of pressure.

For a real gas going through an adiabatic reversible process, the process equation is given by

, where P is the pressure, V is the volume and

is the ratio of the specific heats of the gas at constant pressure and constant volume.

For an ideal gas undergoing a reversible polytropic process

, the equation connecting the pressure, volume and temperature of the gas at any point along the process is

, where

is the gas constant and

is the mass of the gas.

Any real gas behaves as an ideal gas at sufficiently low pressure or sufficiently high temperature.

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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

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

. The initial pressure of the air inside the cylinder is

, where

is the atmospheric pressure. The stop

is instantaneously removed and the piston moves to the position

, where the equilibrium pressure of air inside the cylinder is

What is the work done by the piston on the atmosphere during this process?

Diagram for Mechanical Engineering question 42

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A cylindrical rod of length

and diameter

is placed inside a cubic enclosure of side length

denotes the inner surface of the cube. The view-factor

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In an ideal orthogonal cutting experiment (see figure), the cutting speed V is 1 m/s, the rake angle of the tool

, and the shear angle,

, is known to be

Applying the ideal orthogonal cutting model, consider two shear planes PQ and RS close to each other. As they approach the thin shear zone (shown as a thick line in the figure), plane RS gets sheared with respect to PQ (point R1 shears to R2, and S1 shears to S2).

Assuming that the perpendicular distance between PQ and RS is

m, what is the value of shear strain rate (in s

) that the material undergoes at the shear zone?

Diagram for Mechanical Engineering question 44

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A CNC machine has one of its linear positioning axes as shown in the figure, consisting of a motor rotating a lead screw, which in turn moves a nut horizontally on which a table is mounted. The motor moves in discrete rotational steps of 50 steps per revolution. The pitch of the screw is 5 mm and the total horizontal traverse length of the table is 100 mm. What is the total number of controllable locations at which the table can be positioned on this axis?

Diagram for Mechanical Engineering question 45

Your answerChoose one option.

5000

1000

200

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GATE ME branch:me PYQs

Question 36

Question 37

Question 38

Question 39

Question 40

Question 41

Question 42

Question 43

Question 44

Question 45