GATE ME format:mcq PYQs & Answers — Page 22

Questions 211–220 of 599. Imported answers require independent review unless marked reviewed.

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

Your answerChoose one option.

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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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In Fe-Fe₃C phase diagram, the eutectoid composition is 0.8 weight % of carbon at 725 °C. The maximum solubility of carbon in α-ferrite phase is 0.025 weight % of carbon. A steel sample, having no other alloying element except 0.5 weight % of carbon, is slowly cooled from 1000 °C to room temperature. The fraction of pro-eutectoid α-ferrite in the above steel sample at room temperature is

Your answerChoose one option.

0.387

0.864

0.475

0.775

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Parts P1-P7 are machined first on a milling machine and then polished at a separate machine. Using the information in the following table, the minimum total completion time required for carrying out both the operations for all 7 parts is ______ hours.

Part	Milling (hours)	Polishing (hours)
P1	8	6
P2	3	2
P3	3	4
P4	4	6
P5	5	7
P6	6	4
P7	2	1

Your answerChoose one option.

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Activities A to K are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is to be completed in the minimum possible time, the latest finish time for the activity G is ____________ hours.

Activity	Time (hours)	Immediate predecessors
A	2	—
B	3	—
C	2	—
D	4	A
E	5	B
F	4	B
G	3	C
H	10	D, E
I	5	F
J	8	G
K	3	H, I, J

Your answerChoose one option.

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A manufacturing unit produces two products P1 and P2. For each piece of P1 and P2, the table below provides quantities of materials M1, M2, and M3 required, and also the profit earned. The maximum quantity available per day for M1, M2 and M3 is also provided. The maximum possible profit per day is ₹__________.

	M1	M2	M3	Profit per piece (₹)
P1	2	2	0	150
P2	3	1	2	100
Maximum quantity available per day	70	50	40

Your answerChoose one option.

5000

4000

3000

6000

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A solid spherical bead of lead (uniform density = 1100 kg/m

) of diameter

mm sinks with a constant velocity

in a large stagnant pool of a liquid (dynamic viscosity =

kg·m

·s

). The coefficient of drag is given by

, where the Reynolds number (Re) is defined on the basis of the diameter of the bead. The drag force acting on the bead is expressed as

, where

is the density of the liquid. Neglect the buoyancy force. Using

m/s

, the velocity

is ________ m/s.

Your answerChoose one option.

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A tube of uniform diameter

is immersed in a steady flowing inviscid liquid stream of velocity

, as shown in the figure. Gravitational acceleration is represented by

. The volume flow rate through the tube is _____.

Diagram for Mechanical Engineering question 43

Your answerChoose one option.

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GATE ME format:mcq PYQs

Question 39

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Question 40

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Question 42

Question 43

Question 43