GATE ME topic:mechanical-engineering PYQs & Answers — Page 61

Questions 601–610 of 1040. Imported answers require independent review unless marked reviewed.

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

Your answerChoose one option.

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A helical spring has spring constant

. If the wire diameter, spring diameter and the number of coils are all doubled then the spring constant of the new spring becomes

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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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Two rollers of diameters

(in mm) and

(in mm) are used to measure the internal taper angle in the V-groove of a machined component. The heights

(in mm) and

(in mm) are measured by using a height gauge after inserting the rollers into the same V-groove as shown in the figure.

Diagram for Mechanical Engineering question 32

Which one of the following is the correct relationship to evaluate the angle

as shown in the figure?

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For an assembly line, the production rate was 4 pieces per hour and the average processing time was 60 minutes. The WIP inventory was calculated. Now, the production rate is kept the same, and the average processing time is brought down by 30 percent. As a result of this change in the processing time, the WIP inventory

Your answerChoose one option.

decreases by 25%

increases by 25%

decreases by 30%

increases by 30%

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The forecast for the monthly demand of a product is given in the table below.

Month	Forecast	Actual Sales
1	32.00	30.00
2	31.80	32.00
3	31.82	30.00

The forecast is made by using the exponential smoothing method. The exponential smoothing coefficient used in forecasting the demand is

Your answerChoose one option.

0.10

0.40

0.50

1.00

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A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density and specific heat of the metal are 8500 kg/m³ and 400 J/kg.K, respectively. If the bead is considered as a lumped system, the convective heat transfer coefficient (in W/m².K) between the metal bead and the fluid stream is

Your answerChoose one option.

283.3

299.8

149.9

449.7

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One kg of air in a closed system undergoes an irreversible process from an initial state of

bar (absolute) and

, to a final state of

bar (absolute) and

. If the gas constant of air is 287 J/kg.K and the ratio of the specific heats

, then the change in the specific entropy (in J/kg.K) of the air in the process is

Your answerChoose one option.

indeterminate, as the process is irreversible

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Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is ______ (round off to 2 decimal places).

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For the integral

, the absolute percentage error in numerical evaluation with the Trapezoid rule, using only the end points, is ______ (round off to one decimal place).

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GATE ME topic:mechanical-engineering PYQs

Question 31

Question 31

Question 32

Question 32

Question 33

Question 33

Question 34

Question 34

Question 35

Question 35