GATE ME 2020 Paper 1 — page 14

Questions 40–42 of 65. Imported answers require review unless explicitly marked reviewed.

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

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A rigid mass-less rod of length

is connected to a disc (pulley) of mass

and radius

through a friction-less revolute joint. The other end of that rod is attached to a wall through a friction-less hinge. A spring of stiffness

is attached to the rod at its mid-span. An inextensible rope passes over half the disc periphery and is securely tied to a spring of stiffness

at point C as shown in the figure. There is no slip between the rope and the pulley. The system is in static equilibrium in the configuration shown in the figure and the rope is always taut.

Diagram for Mechanical Engineering question 31

Neglecting the influence of gravity, the natural frequency of the system for small amplitude vibration is

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A strip of thickness 40 mm is to be rolled to a thickness of 20 mm using a two-high mill having rolls of diameter 200 mm. Coefficient of friction and arc length in mm, respectively, are

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0.45 and 38.84

0.39 and 38.84

0.39 and 44.72

0.45 and 44.72

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2020 · Paper 1

Question 30

Question 31

Question 32