GATE ME topic:engineering-mechanics PYQs & Answers — Page 3

Questions 21–30 of 61. Imported answers require independent review unless marked reviewed.

A rigid body in the X-Y plane consists of two point mass (1 kg each) attached to the ends of two massless rods, each of 1 cm length, as shown in the figure. It rotates at 30 RPM counter-clockwise about the Z-axis passing through point O. A point mass of

kg, attached to one end of a third massless rod, is used for balancing the body by attaching the free end of the rod to point O. The length of the third rod is ______ cm.

Diagram for Mechanical Engineering question 39

Your answerChoose one option.

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The lengths of members BC and CE in the frame shown in the figure are equal. All the members are rigid and lightweight, and the friction at the joints is negligible. Two forces of magnitude

are applied as shown, each at the mid-length of the respective member on which it acts. Which one or more of the following members do not carry any load (force)?

Diagram for Mechanical Engineering question 47

Your answerSelect all correct options. You can choose more than one.

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Consider two vectors:

Magnitude of the component of

orthogonal to

in the plane containing the vectors

and

is _________ (round off to 2 decimal places).

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A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. AE is a single member that contains pin C. Likewise, BE is a single member that contains pin D. Members GI and FH are overlapping rigid members. The magnitude of the force carried by member CI is ________ kN (in integer).

Diagram for Mechanical Engineering question 49

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Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectively, as shown in the figure. A vertical force

acts on the pin R as shown. When the included angle

, the rods remain in static equilibrium due to Coulomb friction between the rods and ground at locations P and Q. At

, impending slip occurs simultaneously at points P and Q. Then the ratio of the coefficient of friction at Q to that at P (

) is _________ (round off to two decimal places).

Diagram for Mechanical Engineering question 50

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A cylindrical disc of mass

kg and radius

m was spinning at

rad/s when it was placed on a flat horizontal surface and released (refer to the figure). Gravity

acts vertically downwards as shown in the figure. The coefficient of friction between the disc and the surface is finite and positive. Disregarding any other dissipation except that due to friction between the disc and the surface, the horizontal velocity of the center of the disc, when it starts rolling without slipping, will be ________ m/s (round off to 2 decimal places).

Diagram for Mechanical Engineering question 51

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A plane truss

(

and

) is shown in the figure. The forces in the members

and

, respectively, are

Diagram for Mechanical Engineering question 14

Your answerChoose one option.

(tensile) and

(tensile)

(tensile) and

(compressive)

(compressive) and

(compressive)

(tensile) and

(tensile)

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Consider a two degree of freedom system as shown in the figure, where

is a rigid uniform rod of length,

and mass,

Diagram for Mechanical Engineering question 30

Assume that the spring deflects only horizontally and force

is applied horizontally at

. For this system, the Lagrangian,

Your answerChoose one option.

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Two smooth identical spheres each of radius 125 mm and weight 100 N rest in a horizontal channel having vertical walls. The distance between vertical walls of the channel is 400 mm.

The reaction at the point of contact between two spheres is ______ N (round off to one decimal place).

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A block of negligible mass rests on a surface that is inclined at 30° to the horizontal plane as shown in the figure. When a vertical force of 900 N and a horizontal force of 750 N are applied, the block is just about to slide.

The coefficient of static friction between the block and surface is __________ (round off to two decimal places).

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GATE ME topic:engineering-mechanics PYQs

Question 39

Question 47

Question 48

Question 49

Question 50

Question 51

Question 14

Question 30

Question 50

Question 51