# GATE mechanical practice paper - 1

1)   An object of 1 kg is attached to the string at the height of 100 m from the ground. What is the velocity of the object when it impacts on the ground, if it is released from string at 100 m?
Take acceleration due to gravity g=9.8 m/s2 (Marks: 02)

a. 1960 m/s
b. 221.36 m/s
c. 44.27 m/s
d. none of the above
 Answer  Explanation ANSWER: 44.27 m/s Explanation: No other than gravitational force is acting upon the object. Thus by using motion equation v2 = u2+ 2as and taking initial velocity of the object u = 0, we can get the final velocity that is 44.27 m/s.

2)   Two velocities are moving in such direction that the angle between them is 30°. The two velocities are having magnitudes 15 m/s and 25 m/s respectively. Calculate the magnitude of resultant velocity. (Marks: 02)

a. 30.47 m/s
b. 35 m/s
c. 38.72 m/s
d. none of the above
 Answer  Explanation ANSWER: 38.72 m/s Explanation: By using parallelogram law,w2 =u2 + v2 + 2uv cos(a)Where,w = magnitude of resultant velocityu = magnitude of first velocityv = magnitude of second velocitya = angle between first and second velocity

3)   What is stress? (Marks: 01)

a. internal resistance offered by a body against deformation
b. external resistance offered by a body against deformation
c. internal force offered by a body against deformation
d. external force offered by a body against deformation
 Answer  Explanation ANSWER: internal resistance offered by a body against deformation Explanation: Stress is an internal resistance offered by a body or a material against deformation. It is a resisting force per unit area.

4)   Poisson's ratio is the ratio of ______(Marks: 01)

a. longitudinal strain to lateral strain
b. lateral strain to longitudinal strain
c. longitudinal stress to lateral strain
d. lateral stress to longitudinal strain
 Answer  Explanation ANSWER: lateral strain to longitudinal strain Explanation: The ratio of lateral strain to longitudinal strain has a constant value and it is called as Poisson's ratio. Poisson's ratio is denoted by v

5)   A spring of radius 1 cm obeys Hooke's law. A mass of 2 kg is attached to the spring. Calculate the extension of the spring. The spring constant k is 110 N/m

a. 17.81 m
b. 0.1781 cm
c. 0.1781 m
d. 0.1781 mm
 Answer  Explanation ANSWER: 0.1781 m Explanation: According to the Hooke's law force applied to extend or compress a spring is directly proportional to change in length of the spring. Therefore F = – kX where k is spring constant. By using this formula and taking force applied F = mg = 2 × 9.8 =19.6 N and k = 110 N/m we can fine X.

6)   Calculate the normal stress acting on the plane of maximum shear stress, considering the following state of stress shown in the figure. (Marks: 02)

a. 30 MPa compression
b. 30 MPa tension
c. 15 MPa compression
d. 15 MPa tension
 Answer  Explanation ANSWER: 15 MPa compression Explanation: Normal stress acting on the plane of maximum shear stress will be, (Taking compression as positive)σn = (σx± σy) / 2 =(50 – 20) / 2 = +15that is 15 MPa compression.

7)   The part of machine which is resistant and undergoes relative motion is called as __________(Marks: 01)

b. element
c. both a. and b.
d. none of the above
 Answer  Explanation ANSWER: both a. and b. Explanation: A part of machine which undergoes relative motion with respect to some other part is called as as kinematic link or element. The kinematic link or element should be resistant body.

8)   How is the kinematic pair formed?(Marks: 01)

a. when two kinematic links of a machine are in contact with each other and relative motion between them is not completely constrained
b. when two kinematic links of a machine are in contact with each other and relative motion between them is completely constrained
c. both a. and b.
d. none of the above
 Answer  Explanation ANSWER: when two kinematic links of a machine are in contact with each other and relative motion between them is completely constrained Explanation: When two kinematic links or elements are in contact with each other, they are said to form a pair and if the relative motion between them is completely constrained, the pair is called as kinematic pair.

9)   The punching rate of a punching press is 20 holes per minute. It is required to punch a hole of diameter 50 mm on a plate of 20 mm thickness. Press requires 10 N-m of energy per mm2 of sheared area. Calculate the energy required for punching work per second. (Marks: 02)

a. 628318.2 Nm/s
b. 10471.97 Nm/s
c. 31416 Nm/s
d. none of the above
 Answer  Explanation ANSWER: 10471.97 Nm/s Explanation: d =50 mmt = 20 mmNumber of holes = 20 holes per minuteEnergy required = 10 N-m/mm 2Sheared area per hole = πdt= π × 50 × 20= 3141.6 mm2Energy required to punch one hole = 3141.6 × 10= 31416 N-mand the energy required for punching work per second= energy required per hole × number of holes per second= 31416 × (20/60)= 10471.97 Nm/s

10)   Which of the following statements is wrong?

(1) A statically balanced rotor is always dynamically balanced
(2) A dynamically balanced rotor is always statically balanced (Marks: 02)

a. Only (1)
b. Only (2)
c. both (1) and (2)
d. both are correct
 Answer  Explanation ANSWER: Only (1) Explanation: When rotor is dynamically balanced then it is always statically balanced. But when rotor is statically balanced then it may or may not be dynamically balanced.

11)   The ratio of critical stress to allowable stress is called as ___________(Marks: 01)

a. factor of stress
b. factor of strength
c. factor of safety
d. none of the above
 Answer  Explanation ANSWER: factor of safety Explanation: Factor of safety is the ratio of critical stress (or ultimate stress) to allowable stress (or working stress). Higher the value of factor of safety, lower will be the risk of failure of machine element.

12)   The load which can vary in magnitude as well as in direction is called as ________(Marks: 01)

c. both a. and b.
d. none of the above

13)   Why is the maximum stress applied to any machine element should always be less than its ultimate stress or critical stress? (Marks: 02)

a. for safety against machine failure
b. to make complete use of mechanical properties of the machine element
c. both a. and b
d. none of the above
 Answer  Explanation ANSWER: both a. and b Explanation: To design any machine element, safety is always considered as an important factor. Also to make use of mechanical properties of the machine element before its failure, it is designed in such a manner that the maximum applied stress should be less than its ultimate stress or critical stress. This applied stress is called as allowable stress or working stress.

14)   Maximum principles stress theory by Rankine is applicable for those materials which are __________(Marks: 02)

a. strong in shear but weak in tension or compression
b. weak in shear but strong in tension or compression
c. strong in shear as well as in tension or compression
d. weak in shear as well as in tension or compression
 Answer  Explanation ANSWER: strong in shear but weak in tension or compression Explanation: The Rankine theory predicts the failure behavior of brittle material like cast iron. Brittle materials are strong in shear but weak in tension or compression.

15)   What is the effect of plating on the fatigue strength of a machine element?(Marks: 02)

a. plating increases fatigue strength of a machine element
b. plating decreases fatigue strength of a machine element
c. plating does not affect fatigue strength of a machine element
d. unpredictable
 Answer  Explanation ANSWER: plating decreases fatigue strength of a machine element Explanation: The internal residual stresses importantly affect the fatigue strength of a machine element. These internal residual stresses are affected by plating. Thus plating decreases fatigue strength of a machine element.

16)   The ratio of weight of fluid to the volume of the fluid is called as _________(Marks: 01)

a. partial weight
b. partial volume
c. specific weight
d. specific volume
 Answer  Explanation ANSWER: specific weight Explanation: Specific weight is defined as the weight of the fluid per unit volume.

17)   Which of the following is actually an ideal fluid?(Marks: 02)

a. air
b. water
c. oil
d. none of the above
 Answer  Explanation ANSWER: none of the above Explanation: The fluid which is incompressible and which has no viscosity is known as an ideal fluid. Water and oil have some viscosity among the above fluids. Viscosity of air can be negligible but it is not incompressible. Therefore ideal fluid is only a hypothetical fluid. All the existing fluids have some viscosity.

18)   The velocity at which the fluid flow changes from viscous flow to a turbulent flow is called as ___________(Marks: 02)

a. laminar velocity of fluid flow
b. turbulent velocity of fluid flow
c. critical velocity of fluid flow
d. none of the above
 Answer  Explanation ANSWER: critical velocity of fluid flow Explanation: A liquid have steady viscous flow at only low velocity. The flow becomes turbulent after reaching certain velocity. This velocity is called as critical velocity of fluid flow.

19)   Which among the following sentences are true for turbulent flow

(1) The frictional resistance is proportional to the square of the velocity
(2) The frictional resistance is independent of the pressure
(3) The frictional resistance is proportional to the density of fluid
(4) The frictional resistance slightly varies with temperature   (Marks: 02)

a. sentences (1), (2) and (3) are correct
b. sentences (2), (3) and (4) are correct
c. sentences (1), (2) and (4) are correct
d. all the sentences are correct
 Answer  Explanation ANSWER: all the sentences are correct Explanation: The laws of friction for turbulent flow states that, the frictional resistance is proportional to the square of the velocity, the frictional resistance is independent of the pressure, the frictional resistance is proportional to the density of fluid and the frictional resistance slightly varies with temperature

20)   A copper plat has dimensions 1m × 2m × 0.08m. The one of the largest surfaces is kept at 100 °C and other one is at 0 °C. Thermal conductivity of the copper plate k is 400 W/mK. What is the rate at which energy flows through the plate and the thermal resistance of the plate? (Marks: 02)

a. 800 kW, 1 × 10– 3 K/W
b. 800 kW, 1 × 10– 4 K/W
c. 80000 W, 1 × 10– 3 K/W
d. 80000 W, 1 × 10– 4 K/W
 Answer  Explanation ANSWER: 800 kW, 1 × 10– 4 K/W Explanation: According to the Fourier's law of heat conduction,Rate of heat flow is given by,qk = ( k A ΔT ) / l= (400 × 1 × 2 × (80 – 0)) / 0.08=800 kWAnd thermal resistance is given by,Rt = l / kA= 0.08 / (400 × 1 × 2)=1 × 10– 4 K/W

21)   Two layers of different metals are made composite connecting parallel. The heat flow takes place as shown in figure. Thermal resistances of the two layers are R1 = 0.036 K/W and R2 = 0.05 K/W What is the thermal resistance of the system?  (Marks: 02)

a. 0.086 K/W
b. 47.778 K/W
c. 0.0209 K/W
d. none of the above
 Answer  Explanation ANSWER: 0.0209 K/W Explanation: In a composite wall when layers are connected in parallel, the thermal resistance of the system is given by,(1 / R) = (1 / R2) + (1 / R2)R = (R1 × R2) / (R1 + R2) R = (0.036 × 0.05) + (0.036 + 0.05)R = 0.0209 K/W

22)   In which condition does the internal energy of the system increase? (Marks: 02)

a. when the heat transfer into the system is less than the work transfer out of the system
b. when the heat transfer into the system is more than the work transfer out of the system
c. when the heat transfer into the system is equal to the work transfer out of the system
d. none of the above
 Answer  Explanation ANSWER: when the heat transfer into the system is more than the work transfer out of the system Explanation: When a system undergoes a change of state along with the heat transfer as well as work transfer, the net energy transfer is collected and stored within the system. When heat transfer within the system Q is more than the work transfer out of the system W, then the change in energy (Q – W) is stored in the system. This is the internal energy and it increases.

23)   Which is the example of path function?(Marks: 01)

a. Heat energy
b. Work energy
c. both a. and b.
d. none of the aboves
 Answer  Explanation ANSWER: both a. and b. Explanation: Heat energy as well as work energy both depend on the path followed by the system. Therefore both are the path functions.

24)   What is the Perpetual Motion Machine of First Kind (PMM1)? (Marks: 02)

a. a machine which produces mechanical work with consumption of some energy
b. a machine which produces mechanical work without consumption of some energy
c. a machine which generates heat energy with consumption of some external work
d. none of the above
 Answer  Explanation ANSWER: a machine which produces mechanical work without consumption of some energy Explanation: PMM1 is a machine which violates first law of thermodynamics. It states that energy neither be created nor be destroyed. Thus PMM1 is a machine which produces mechanical work without consumption of some energy

25)   A cyclic heat engine operates between source temperature of 1000 °C and a sink temperature 50 °C. Calculate least rate of heat rejection when net work output is 2 kW. (Marks: 02)

a. 2.6799 kW
b. 0.6799 kW
c. 0.7463 kW
d. none of the above
 Answer  Explanation ANSWER: 0.6799 kW Explanation: The rate of heat rejection will be least for reversible engine, ηrev = ηmax = 1 – (Tsink / Tsource )= 1 – (323 / 1273) = 0.7463ηmax = Wnet / Q1Q1 = Wnet / ηmax = 2 / 0.7463= 2.6799 kWTherefore the least heat rejection rate, Q2 is Q2 = Q1 – Wnet= 2.6799 – 2 = 0.6799 kW

26)   What is a quasi-static process? (Marks: 02)

a. a process which is random
b. a process which is spontaneous
c. a process which is infinitely slow
d. a process which is stationary
 Answer  Explanation ANSWER: a process which is infinitely slow Explanation: The system has to pass through an infinitely slow process in order to experience equilibrium at every stage in the process. This infinitely slow process is called as quasi-static process

27)   Which among the following has an infinite heat capacity?(Marks: 01)

a. heat engine
b. thermal energy reservoir
c. both a. and b
d. none of the above
 Answer  Explanation ANSWER: thermal energy reservoir Explanation: Thermal energy reservoir is either heat source or heat sink which can absorb or reject unlimited amount of heat energy without considerable change in temperature.

28)   What is the relation between the specific heat of gas at constant pressure (Cv) and the specific heat of gas at constant volume (Cp) at the absolute zero point? (Marks: 02)

a. (Cp) > (Cv)
b. (Cp) < (Cv)
c. (Cp) = (Cv)
d. unpredictable
 Answer  Explanation ANSWER: (Cp) = (Cv) Explanation: The entropy is zero at the absolute zero. Also the value of γ is 1 at the absolute zero. γ = 1 = Cp/ CvTherefore (Cp) = (Cv) at absolute zero

29)   Which condition of Rankine cycle has highest efficiency when operating between same pressure limits? (Marks: 02)

a. Superheated cycle
b. Regenerative cycle
c. Reheat cycle
d. Saturated cycle
 Answer  Explanation ANSWER: Regenerative cycle Explanation: The efficiency of ideal regenerative cycle is exactly equal to the corresponding Carnot cycle. Hence it is maximum.

30)   What is the purpose of using capillary tube in vapor compression refrigeration cycle?(Marks: 01)

a. to compress the refrigerant
b. to expand the refrigerant
c. to condense refrigerant
d. none of the above
 Answer  Explanation ANSWER: to expand the refrigerant Explanation: High pressure condensed refrigerant is expanded in capillary tube or throttling value.

31)   Which parameter is constant during condensation process in vapor compression refrigeration cycle? (Marks: 02)

a. enthalpy
b. volume
c. pressure
d. all of the above
 Answer  Explanation ANSWER: pressure Explanation: Condensation process in vapor compression cycle is a constant pressure process. Refrigerant is first superheated and then condensed.

32)   Mass fraction of vapor in liquid-vapor mixture is called as _________(Marks: 02)

a. partial gas fraction
b. flash gas fraction
c. both a. and b.
d. none of the above
 Answer  Explanation ANSWER: flash gas fraction Explanation: Flash gas fraction is the quality of refrigerant at the inlet to the evaporator. This is the mass fraction of vapor in liquid-vapor mixture of refrigerant.

33)   What is the cause of formation of blow holes in metal casting? (Marks: 02)

a. excessive moisture
b. presence of such ingredients which produce gas
c. fine grains
d. all of the above
 Answer  Explanation ANSWER: all of the above Explanation: Blow holes appear as cavities in the casting. They are the entrapped bubbles of gases caused by excessive moisture, gas producing ingredients as well as fine grains.

34)   The forming process in which the working temperature is lower than the recrystallization temperature is called as ________(Marks: 01)

a. hot forming
b. cold forming
c. crystalline forming
d. none of the above
 Answer  Explanation ANSWER: cold forming Explanation: In cold working or cold forming the plastic deformation of metal is carried out at the temperature below recrystallization temperature.

35)   Which is the material represented in below stress-strain curve? (Marks: 02)

a. Rigid ideal plastic material
b. Ideal plastic material with elastic region
c. Ideal elastic material
d. none of the above
 Answer  Explanation ANSWER: Ideal plastic material with elastic region Explanation: In above diagram, the material behaves elastically at certain point and after that it behaves as ideal plastic material. Thus it is an ideal plastic material with elastic region.

36)   Which of the following is NOT a type of hot working?(Marks: 01)

a. Rolling
b. Pipe welding
c. Forging
d. none of the above
 Answer  Explanation ANSWER: none of the above Explanation: All the given processes are types of hot working.

37)   What is the effect of hot working process on material density? (Marks: 02)

a. material density decreases in hot working process
b. material density increases in hot working process
c. material density remains same in hot working process
d. unpredictable
 Answer  Explanation ANSWER: material density increases in hot working process Explanation: Any pores or cavity in the cast metal disappear in hot working process. This results in increase in material density.

38)   What is the effect of cold working process on material grains? (Marks: 02)

a. material grains distort permanently
b. material grains distort temporarily and again come back to original shape slowly
c. material grains remains as it is
d. can't say
 Answer  Explanation ANSWER: material grains distort permanently Explanation: There is no crystallization takes place in cold working process. Material is processed mechanically below crystallization temperature. Thus material grains are permanently distorted.

39)   Which process is best suitable to increase strength of material and to decrease ductility after processing? (Marks: 02)

a. Hot working
b. Cold working
c. both a. and b.
d. none of the above
 Answer  Explanation ANSWER: Cold working Explanation: The material grains are permanently distorted in cold working process. The material strength increases and ductility decreases in cold working process.

40)   Why is the copper suitable to use as filler for joining iron and silver? (Marks: 02)

a. copper is soluble in iron
b. copper is soluble in silver
c. both a. and b.
d. none of the above
 Answer  Explanation ANSWER: both a. and b. Explanation: The filler material should be soluble in both of the materials which are going to be joined. As copper is soluble in iron as well as in silver, it is suitable as filler for joining iron and silver.

41)   Which type of material is difficult to spot weld? (Marks: 02)

a. highly resistive materials
b. highly conductive materials
c. both a. and b.
d. none of the above
 Answer  Explanation ANSWER: highly conductive materials Explanation: Spot welding requires maximum resistance at the surface of two parts to be joined. Thus spot welding process is difficult for highly conductive materials