GATE ME topic:mechanics PYQs & Answers — Page 34

Questions 331–340 of 1040. Imported answers require independent review unless marked reviewed.

The value of the integral

evaluated over a counter-clockwise circular contour in the complex plane enclosing only the pole

, where

is the imaginary unit, is

Your answerChoose one option.

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For the exact differential equation,

which one of the following is the solution?

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An L-shaped elastic member ABC with slender arms AB and BC of uniform cross-section is clamped at end A and connected to a pin at end C. The pin remains in contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end C is subjected to a horizontal force

and all the deflections are in the plane of the figure. Given the length AB is

and length BC is

, the magnitude and direction of the normal force on the pin from the slot, respectively, are

Diagram for Mechanical Engineering question 37

Your answerChoose one option.

, and downwards

, and upwards

, and downwards

, and upwards

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A rigid homogeneous uniform block of mass 1 kg, height

m and width

m is pinned at one corner and placed upright in a uniform gravitational field (

m/s

), supported by a roller in the configuration shown in the figure. A short duration (impulse) force

, producing an impulse

, is applied at a height of

m from the bottom as shown. Assume all joints to be frictionless. The minimum value of

required to topple the block is

Your answerChoose one option.

0.953 Ns

1.403 Ns

0.814 Ns

1.172 Ns

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A planar four-bar link mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB ⟂ CE and FD ⟂ CE. The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is

Diagram for Mechanical Engineering question 38

Your answerChoose one option.

a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG

a non-Grashof chain with all oscillating links

a Grashof chain with AB completely rotatable about the ground link FG, and oscillatory links AG and CDEF

on the border of Grashof and non-Grashof chains with uncertain configuration(s)

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A linear elastic structure under plane stress condition is subjected to two sets of loading, I and II. The resulting states of stress at a point corresponding to the two loads are shown in the figure below. If these two sets of loading are applied simultaneously, then the net normal component of stress

is ______.

Your answerChoose one option.

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Consider a forced single degree-of-freedom system governed by

, where

and

are the damping ratio and undamped natural frequency of the system, respectively, while

is the forcing frequency. The amplitude of the forced steady state response of this system is given by

, where

. The peak amplitude of this response occurs at a frequency

. If

denotes the damped natural frequency of this system, which one of the following options is true?

Your answerChoose one option.

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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

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A bracket is attached to a vertical column by means of two identical rivets U and V separated by a distance of

mm, as shown in the figure. The permissible shear stress of the rivet material is 50 MPa. If a load

kN is applied at an eccentricity

, the minimum cross-sectional area of each of the rivets to avoid failure is

Diagram for Mechanical Engineering question 40

________ mm².

Your answerChoose one option.

800

200

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A spring mass damper system (mass

, stiffness

, and damping coefficient

) excited by a force

, where

and

are the amplitude, frequency and time, respectively, is shown in the figure. Four different responses of the system (marked as (i) to (iv)) are shown just to the right of the system figure. In the figures of the responses,

is the amplitude of response shown in red color and the dashed lines indicate its envelope. The responses represent only the qualitative trend and these are not drawn to any specific scale.

Four different parameter and forcing conditions are mentioned below.

(P)

and

(Q)

and

(R)

and

(S)

and

Which one of the following options gives correct match (indicated by arrow →) of the parameter and forcing conditions to the responses?

Your answerChoose one option.

(P) → (i), (Q) → (iii), (R) → (iv), (S) → (ii)

(P) → (ii), (Q) → (iii), (R) → (iv), (S) → (i)

(P) → (i), (Q) → (iv), (R) → (ii), (S) → (iii)

(P) → (iii), (Q) → (iv), (R) → (ii), (S) → (i)

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GATE ME topic:mechanics PYQs

Question 36

Question 36

Question 37

Question 37

Question 38

Question 38

Question 39

Question 39

Question 40

Question 40