GATE ME topic:mechanics PYQs & Answers — Page 62

Questions 611–620 of 1040. Imported answers require independent review unless marked reviewed.

Topic practice 1040 questionsPage 62 of 104

An analytic function of a complex variable z = x + iy (i = √−1) is defined as

where ψ(x,y) is a real function. The value of the imaginary part of f(z) at z = (1 + i) is ______ (round off to 2 decimal places).

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A fair coin is tossed 20 times. The probability that ‘head’ will appear exactly 4 times in the first ten tosses, and ‘tail’ will appear exactly 4 times in the next ten tosses is ______ (round off to 3 decimal places).

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In a disc-type axial clutch, the frictional contact takes place within an annular region with outer and inner diameters 250 mm and 50 mm, respectively. An axial force F₁ is needed to transmit a torque by a new clutch. However, to transmit the same torque, one needs an axial force F₂ when the clutch wears out. If contact pressure remains uniform during operation of a new clutch while the wear is assumed to be uniform for an old clutch, and the coefficient of friction does not change, then the ratio F₁/F₂ is ______ (round off to 2 decimal places).

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A hollow spherical ball of radius 20 cm floats in still water, with half of its volume submerged. Taking the density of water as 1000 kg/m

, and the acceleration due to gravity as 10 m/s

, the natural frequency of small oscillations of the ball, normal to the water surface is ______ radians (round off to 2 decimal places).

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A cam with a translation flat-face follower is desired to have the follower motion

Contact stress considerations dictate that the radius of curvature of the cam profile should not be less than 40 mm anywhere. The minimum permissible base circle radius is ______ mm (round off to one decimal place).

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Uniaxial compression test data for a solid metal bar of length 1 m is shown in the figure.

Diagram for Mechanical Engineering question 38

The bar material has a linear elastic response from O to P followed by a nonlinear response. The point P represents the yield point of the material. The rod is pinned at both the ends. The minimum diameter of the bar so that it does not buckle under axial loading before reaching the yield point is ______ mm (round off to one decimal place).

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A rectangular steel bar of length 500 mm, width 100 mm, and thickness 15 mm is cantilevered to a 200 mm steel channel using 4 bolts, as shown.

Diagram for Mechanical Engineering question 39

For an external load of 10 kN applied at the tip of the steel bar, the resultant shear load on the bolt at B, is ______ kN (round off to one decimal place).

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The turning moment diagram of a flywheel fitted to a fictitious engine is shown in the figure.

The mean turning moment is 2000 Nm. The average engine speed is 1000 rpm. For fluctuation in the speed to be within

of the average speed, the mass moment of inertia of the flywheel is ______ kg.m

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The barrier shown between two water tanks of unit width (1 m) into the plane of the screen is modeled as a cantilever.

Diagram for Mechanical Engineering question 40

Taking the density of water as 1000 kg/m³, and the acceleration due to gravity as 10 m/s², the maximum absolute bending moment developed in the cantilever is ______ kN·m (round off to the nearest integer).

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A rigid block of mass

kg having velocity

m/s strikes a stationary block of mass

kg after traveling 1 m along a frictionless horizontal surface as shown in the figure.

The two masses stick together and jointly move by a distance of 0.25 m further along the same frictionless surface, before they touch the mass-less buffer that is connected to the rigid vertical wall by means of a linear spring having a spring constant

N/m. The maximum deflection of the spring is ______ cm (round off to 2 decimal places).

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GATE ME topic:mechanics PYQs

Question 36

Question 36

Question 37

Question 37

Question 38

Question 38

Question 39

Question 39

Question 40

Question 40