GATE ME year:2022 PYQs & Answers — Page 7

Questions 61–70 of 130. Imported answers require independent review unless marked reviewed.

Topic practice 130 questionsPage 7 of 13

The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through O. Its mass moment of inertia is equal to 0.1 kg·cm

about O. A point mass of 0.001 kg hits it normally at 200 cm/s at the location shown, and sticks to it immediately after the impact, the angular velocity of the rod is ________ rad/s (in integer).

Diagram for Mechanical Engineering question 31

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For a dynamical system governed by the equation,

the damping ratio

is equal to

. The displacement

of this system is measured during a hammer test. A displacement peak in the positive displacement direction is measured to be 4 mm. Neglecting higher powers (>1) of the damping ratio, the displacement at the next peak in the positive direction will be ______ mm (in integer).

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A rigid uniform annular disc is pivoted on a knife edge A in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in the plane of the figure without slip at the pivot point. The inner radius

and outer radius

are such that

, and the acceleration due to gravity is

. If the time period of small amplitude simple harmonic motion is given by

, where

is the ratio of circumference to diameter of a circle, then

________ (round off to 2 decimal places).

Diagram for Mechanical Engineering question 32

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An electric car manufacturer underestimated the January sales of car by 20 units, while the actual sales was 120 units. If the manufacturer uses exponential smoothing method with a smoothing constant of

, then the sales forecast for the month of February of the same year is ______ units (in integer).

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Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below.

Material	Atomic mass (amu)	Valency	Density (g/cm )
Copper	63	2	9
Aluminum	27	3	2.7

Ignore overpotentials, and assume that current efficiency is 100% for both the workpiece materials. Under identical conditions, if the material removal rate (MRR) of copper is 100 mg/s, the MRR of aluminum will be ______________ mg/s (round-off to two decimal places).

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The demand of a certain part is 1000 parts/year and its cost is ₹100/part. The orders are placed based on the economic order quantity (EOQ). The cost of ordering is ₹100/order and the lead time for receiving the orders is 5 days. If the holding cost is ₹20/part/year, the inventory level for placing the orders is ______ parts (round off to the nearest integer).

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A polytropic process is carried out from an initial pressure of 110 kPa and volume of 5 m³ to a final volume of 2.5 m³. The polytropic index is given by

. The absolute value of the work done during the process is ______ kJ (round off to 2 decimal places).

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Consider 1 kg of an ideal gas at 1 bar and 300 K contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume

is equal to 750 J·kg⁻¹·K⁻¹. A stirrer performs 225 kJ of work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be ______ bar (in integer).

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A flat plate made of cast iron is exposed to a solar flux of 600 W/m² at an ambient temperature of 25 °C. Assume that the entire solar flux is absorbed by the plate.

Cast iron has a low temperature absorptivity of 0.21. Use Stefan-Boltzmann constant =

W/m²-K⁴. Neglect all other modes of heat transfer except radiation.

Under the aforementioned conditions, the radiation equilibrium temperature of the plate is ________ °C (round off to the nearest integer).

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Wien’s law is stated as follows:

, where

is 2898 μm·K and

is the wavelength at which the emissive power of a black body is maximum for a given temperature

. The spectral hemispherical emissivity (

) of a surface is shown in the figure below (1 Å = 10⁻¹⁰ m). The temperature at which the total hemispherical emissivity will be highest is ______ K (round off to the nearest integer).

Diagram for Mechanical Engineering question 35

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GATE ME year:2022 PYQs

Question 31

Question 31

Question 32

Question 32

Question 33

Question 33

Question 34

Question 34

Question 35

Question 35