GATE ME format:nat PYQs & Answers — Page 28

Questions 271–280 of 418. Imported answers require independent review unless marked reviewed.

Topic practice 418 questionsPage 28 of 42

Two masses

and

having mass

and

, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses

and

are

and

, respectively. The angle between lines OA and OB is 90°. If

and

, then the balance mass to be placed at a radius of 200 mm is ______ kg (round off to two decimal places).

Diagram for Mechanical Engineering question 38

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Consider an elastic straight beam of length

m, with square cross-section of side

mm, and Young’s modulus

GPa. This straight beam was bent in such a way that the two ends meet, to form a circle of mean radius

. Assuming that Euler-Bernoulli beam theory is applicable to this bending problem, the maximum tensile bending stress in the bent beam is ______ MPa.

Diagram for Mechanical Engineering question 39

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A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link 2 is rotating anticlockwise with a constant angular speed

. Length of different links are:

The magnitude of the angular speed of the output link 4 is

at the instant when link 2 makes an angle of 90° with

as shown. The ratio

is ______ (round off to two decimal places).

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Consider a prismatic straight beam of length

m, pinned at the two ends as shown in the figure.

Diagram for Mechanical Engineering question 40

The beam has a square cross-section of side

mm. The Young’s modulus

GPa, and the coefficient of thermal expansion

. The minimum temperature rise required to cause Euler buckling of the beam is ______ K.

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The probability that a part manufactured by a company will be defective is 0.05. If 15 such parts are selected randomly and inspected, then the probability that at least two parts will be defective is ______ (round off to two decimal places).

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In a UTM experiment, a sample of length 100 mm, was loaded in tension until failure. The failure load was 40 kN. The displacement, measured using the cross-head motion, at failure, was 15 mm. The compliance of the UTM is constant and is given by

m/N. The strain at failure in the sample is ______ %.

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A uniform disc with radius

and a mass of

kg is mounted centrally on a horizontal axle of negligible mass and length of 1.5r. The disc spins counter-clockwise about the axle with angular speed

, when viewed from the right-hand side bearing, Q. The axle precesses about a vertical axis at

in the clockwise direction when viewed from above. Let

and

(positive upwards) be the resultant reaction forces due to the mass and the gyroscopic effect, at bearings P and Q, respectively. Assuming

and

, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is ______.

Diagram for Mechanical Engineering question 41

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At a critical point in a component, the state of stress is given as

MPa,

MPa and all other stress components are zero. The yield strength of the material is 468 MPa. The factor of safety on the basis of maximum shear stress theory is ______ (round off to one decimal place).

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A short shoe external drum brake is shown in the figure. The diameter of the brake drum is 500 mm. The dimensions

and

. The coefficient of friction between the drum and the shoe is 0.35. The force applied on the lever

as shown in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is ______ N·m (round off to two decimal places).

Diagram for Mechanical Engineering question 42

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A uniform thin disk of mass 1 kg and radius 0.1 m is kept on a surface as shown in the figure. A spring of stiffness

N/m is connected to the disk center A and another spring of stiffness

N/m is connected at point B just above point A on the circumference of the disk. Initially, both the springs are unstretched. Assume pure rolling of the disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is ______ rad/s (round off to one decimal place).

Diagram for Mechanical Engineering question 43

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GATE ME format:nat PYQs

Question 38

Question 39

Question 39

Question 40

Question 40

Question 41

Question 41

Question 42

Question 42

Question 43