GATE ME 2020 Paper 1 — page 13

Questions 37–39 of 65. Imported answers require review unless explicitly marked reviewed.

A vector field is defined as

where,

are unit vectors along the axes of a right-handed rectangular/Cartesian coordinate system. The surface integral

(where

is an elemental surface area vector) evaluated over the inner and outer surfaces of a spherical shell formed by two concentric spheres with origin as the center, and internal and external radii of 1 and 2, respectively, is

Your answerChoose one option.

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Bars of square and circular cross-section with 0.5 m length are made of a material with shear strength of 20 MPa. The square bar cross-section dimension is 4 cm × 4 cm and the cylindrical bar cross-section diameter is 4 cm. The specimens are loaded as shown in the figure.

Which specimen(s) will fail due to the applied load as per maximum shear stress theory?

Diagram for Mechanical Engineering question 28

Your answerChoose one option.

Tensile and compressive load specimens

Torsional load specimen

Bending load specimen

None of the specimens

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The 2 kg block shown in figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness 5 N/m. The cord hinged at O is initially unstretched and always remains elastic. The block is given a velocity

of 1.5 m/s perpendicular to the cord. The magnitude of velocity in m/s of the block at the instant the cord is stretched by 0.4 m is

Diagram for Mechanical Engineering question 29

Your answerChoose one option.

0.83

1.07

1.36

1.50

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2020 · Paper 1

Question 27

Question 28

Question 29