GATE ME format:nat PYQs & Answers — Page 24

Questions 231–240 of 418. Imported answers require independent review unless marked reviewed.

Topic practice 418 questionsPage 24 of 42

There are two identical shape machines S

and S

. In machine S

, the width of the workpiece is increased by 10% and the feed is decreased by 10%, with respect to that of S

. If all other conditions remain the same then the ratio of total time per pass in S

and S

will be ______ (round off to one decimal place).

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In a turning process using orthogonal tool geometry, a chip length of 100 mm is obtained for an uncut chip length of 250 mm.

The cutting conditions are: cutting speed = 30 m/min, rake angle = 20°.

The shear plane angle is ______ degrees (round off to one decimal place).

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Bars of 250 mm length and 25 mm diameter are to be turned on a lathe with a feed of 0.2 mm/rev. Each grinding of the tool costs Rs. 20. The time required for each tool change is 1 min. Tool life equation is

(where cutting speed

is in m/min and tool life

is in min). The optimum tool cost per piece for maximum production rate is Rs. ______ (round off to 2 decimal places).

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The thickness of a steel plate with material strength coefficient of 210 MPa, has to be reduced from 20 mm to 15 mm in a single pass in a two-high roll mill with a roll radius of 450 mm and rolling velocity of 28 m/min. If the plate has a width of 200 mm and its strain hardening exponent, n is 0.25, the rolling force required for the operation is ______ kN (round off to 2 decimal places).

Note: Average Flow Stress = Material Strength Coefficient × (True Strain)^n/(1+n)

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A point ‘P’ on a CNC controlled XY- stage is moved to another point ‘Q’ using the coordinate system shown in the figure below and rapid positioning command (G00). A pair of stepping motors with maximum speed of 800 rpm, controlling both the X and Y motion of the stage, are directly coupled to a pair of lead screws, each with a uniform pitch of 0.5 mm. The time needed to position the point ‘P’ to the point ‘Q’ is ______ minutes (round off to 2 decimal places).

Diagram for Mechanical Engineering question 46

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Two business owners Sheta and Ashok run their business in two different states. Each of them, independent of the other, produces two products A and B, sells them at Rs. 2,000 per kg and Rs. 3,000 per kg, respectively, and uses Linear Programming to determine the optimal quantity of A and B to maximize their respective daily revenue. Their constraints are as follows: i) for each business owner, the production process is such that the daily production of A has to be at least as much B, and the upper limit for production of B is 10 kg per day, and ii) the respective state regulations restrict Sheta’s production of A to less than 20 kg per day, and Ashok’s production of A to less than 15 kg per day. The demand of both A and B in both the states is very high and everything produced is sold.

The absolute value of the difference in daily (optimal) revenue of Sheta and Ashok is ______ thousand Rupees (round off to 2 decimal places).

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For a single item inventory system, the demand is continuous, which is 1000 per year. The replenishment is instantaneous and backorders (

units) per cycle are allowed as shown in the figure.

Diagram for Mechanical Engineering question 47

As soon as the quantity (

units) ordered from the supplier is received, the backordered quantity is issued to the customers. The ordering cost is Rs. 300 per order. The carrying cost is Rs. 4 per unit per year. The cost of backordering is Rs. 25 per unit per year. Based on the total cost minimization criteria, the maximum inventory reached in the system is ______ (round off to nearest integer).

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Consider two cases as below.

Case 1: A company buys 1000 pieces per year of a certain part from vendor ‘X’. The changeover time is 2 hours and the price is Rs. 10 per piece. The holding cost rate per part is 10% per year.

Case 2: For the same part, another vendor ‘Y’ offers a design where the changeover time is 6 minutes, with a price of Rs. 5 per piece, and a holding cost rate per part of 100% per year. The order size is 800 pieces per year from ‘X’ and 200 pieces per year from ‘Y’.

Assume the cost of downtime as Rs. 20 per hour. The percentage reduction in the annual cost for Case 2, as compared to Case 1 is ______ (round off to 2 decimal places).

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Consider a flow through a nozzle, as shown in the figure below. The air flow is steady, incompressible and inviscid. The density of air is 1.23 kg/m

. The pressure difference, (

) is ______ kPa (round off to 2 decimal places).

Diagram for Mechanical Engineering question 48

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Consider steady, viscous, fully developed flow of a fluid through a circular pipe of internal diameter

. We know that the velocity profile forms a parabola about the pipe centre line, given by:

m/s, where

is a constant. The rate of kinetic energy (in J/s) at the control surface A-B, as shown in the figure, is proportional to

. The value of

is ______.

Diagram for Mechanical Engineering question 49

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GATE ME format:nat PYQs

Question 44

Question 45

Question 45

Question 46

Question 46

Question 47

Question 47

Question 48

Question 48

Question 49