GATE ME topic:mechanics PYQs & Answers — Page 60

Questions 591–600 of 1040. Imported answers require independent review unless marked reviewed.

The evaluation of the definite integral

by using Simpson’s 1/3rd (one-third) rule with step size

yields

Your answerChoose one option.

0.914

1.248

0.581

0.592

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The directional derivative of

at point

in the direction of vector

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The function

of complex variable

, where

, is given as

. For this function to be analytic,

should be

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A cantilever of length

, and flexural rigidity

, stiffened by a spring of stiffness

, is loaded by a transverse force

, as shown. The transverse deflection under the load is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

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

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The sun (S) and the planet (P) of an epicyclic gear train shown in the figure have identical number of teeth. If the sun (S) and the outer ring (R) gears are rotated in the same direction with angular speed

and

, respectively, then the angular speed of the arm AB is

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

The truss shown in the figure has four members of length

and flexural rigidity

, and one member of length

and flexural rigidity

. The truss is loaded by a pair of forces of magnitude

, as shown in the figure.

The smallest value of

, at which any of the truss members will buckle is

Diagram for Mechanical Engineering question 30

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

A thin-walled cylinder of radius

and thickness

is open at both ends, and fits snugly between two rigid walls under ambient conditions, as shown in the figure.

The material of the cylinder has Young’s modulus

, Poisson’s ratio

, and coefficient of thermal expansion

. What is the minimum rise in temperature

of the cylinder (assume uniform cylinder temperature with no buckling of the cylinder) required to prevent gas leakage if the cylinder has to store the gas at an internal pressure of

above the atmosphere?

Your answerChoose one option.

You can attempt this question now. Sign in to view the answer key, explanations and discussion.Log in to check answer

GATE ME topic:mechanics PYQs

Question 26

Question 26

Question 27

Question 27

Question 28

Question 28

Question 29

Question 29

Question 30

Question 30