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Engineering Mechanics

14 Questions

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q1

MCQ[1 Mark]

A horizontal disk has a radial frictionless slot in which a small block is confined to slide. The disk turns anticlockwise about its centre with a constant angular velocity of $3~rad/s$. If the block slides along the slot with a constant speed of $0.2~m/s$ relative to the slot, then the magnitude of Coriolis acceleration in $m/s^{2}$ is

(A)

1.2

(B)

0.6

(C)

2.4

(D)

0.3

Explanation

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q2

MCQ[2 Marks]

Two structural members are connected by a hinge and they are externally loaded as shown in the figure below. A and B are roller supports, and C is a pin support. Neglecting the mass of the members, the magnitude of the vertical reaction force at C in kN is

(A)

5

(B)

10

(C)

20

(D)

15

Explanation

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q3

NAT[2 Marks]

A block of $50~kg$ mass is on an inclined plane. The block is connected to another hanging mass $M$ by an inextensible massless string through two massless pulleys as shown in the figure below. The coefficient of static friction between the block and the inclined plane is $0.3$. Neglecting pulley friction, the minimum value of $M$ required to start the upward motion of the block is ____ kg (rounded off to 1 decimal place).

Explanation

GATE→2026→Applied Mechanics and Design→Engineering Mechanics

Q4

NAT[2 Marks]

A rigid slender bar, AB, is sliding against two mutually perpendicular frictionless walls, as shown in the figure below. The velocity of A in the downward direction at a given instant is $6~m/s$. At that instant, the magnitude of absolute velocity of the midpoint G is ____ m/s (rounded off to 2 decimal places).

Explanation

GATE→2025→Applied Mechanics and Design→Engineering Mechanics

Q5

MCQ[1 Mark]

A rigid circular disc of radius $r$ (in m) is rolling without slipping on a flat surface as shown in the figure below. The angular velocity of the disc is $\omega$ (in rad $s^{-1}$). The velocities (in m $s^{-1}$) at points O and A, respectively, are

(A)

r\omega\hat{i} \text{ and } 0\hat{i}

(B)

r\omega\hat{i} \text{ and } 0\hat{i}

(C)

r\omega\hat{i} \text{ and } r\omega\hat{i}

(D)

r\omega\hat{i} \text{ and } r\omega\hat{i}

Explanation

GATE→2025→Applied Mechanics and Design→Engineering Mechanics

Q6

MCQ[1 Mark]

A truss structure is loaded as shown in the figure below. Among the options given, which member in the truss is a zero-force member?

(A)

BD

(B)

BC

(C)

BA

(D)

AD

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q7

MCQ[1 Mark]

A ram in the form of a rectangular body of size $l=9~m$ and $b=2~m$ is suspended by two parallel ropes of lengths $7~m$. Assume the center-of-mass of the body is at its geometric center and $g=9.81~m/s^{2}$. For striking the object P with a horizontal velocity of $5~m/s$, what is the angle $\theta$ with the vertical from which the ram should be released from rest?

(A)

67.1^{\circ}

(B)

40.2^{\circ}

(C)

35.1^{\circ}

(D)

79.5^{\circ}

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q8

MCQ[1 Mark]

A rigid massless tetrahedron is placed such that vertex O is at the origin and the other three vertices A, B, and C lie on the coordinate axes as shown in the figure. The body is acted on by three point loads, of which one is acting at A along x-axis and another at point B along y-axis. For the body to be in equilibrium, the third point load acting at point O must be

(A)

along z-axis

(B)

in x-y plane but not along x or y axis

(C)

in y-z plane but not along y or z axis

(D)

in z-x plane but not along z or x axis

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q9

MSQ[2 Marks]

Which of the following beam(s) is/are statically indeterminate?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q10

NAT[2 Marks]

A horizontal beam of length $1200~mm$ is pinned at the left end and is resting on a roller at the other end as shown in the figure. A linearly varying distributed load is applied on the beam. The magnitude of maximum bending moment acting on the beam is ____ N \cdot m (round off to 1 decimal place).

Explanation

GATE→2024→Applied Mechanics and Design→Engineering Mechanics

Q11

NAT[2 Marks]

A three-hinge arch ABC in the form of a semi-circle is shown in the figure. The arch is in static equilibrium under vertical loads $P=100~kN$ and $Q=50~kN$. Neglect friction at all the hinges. The magnitude of the horizontal reaction at B is ____ kN (rounded off to 1 decimal place).

Explanation

GATE→2023→Applied Mechanics and Design→Engineering Mechanics

Q12

MCQ[1 Mark]

The options show frames consisting of rigid bars connected by pin joints. Which of the frames is non-rigid?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2023→Applied Mechanics and Design→Engineering Mechanics

Q13

MCQ[2 Marks]

A spherical ball weighing $2~kg$ is dropped from a height of $4.9~m$ onto an immovable rigid block as shown in the figure. If the collision is perfectly elastic, what is the momentum vector of the ball (in $kg~m/s$) just after impact?\nTake the acceleration due to gravity to be $g=9.8~m/s^{2}$.

(A)

19.6 \hat{i}

(B)

19.6 \hat{j}

(C)

17.0 \hat{i} + 9.8 \hat{j}

(D)

9.8 \hat{i} + 17.0 \hat{j}

Explanation

GATE→2023→Applied Mechanics and Design→Engineering Mechanics

Q14

MCQ[2 Marks]

The figure shows a wheel rolling without slipping on a horizontal plane with angular velocity $\omega_{1}$. A rigid bar PQ is pinned to the wheel at P while the end Q slides on the floor.\nWhat is the angular velocity $\omega_{2}$ of the bar PQ?

(A)

\omega_2 = 2\omega_1

(B)

\omega_2 = \omega_1

(C)

\omega_2 = 0.5\omega_1

(D)

\omega_2 = 0.25\omega_1

Explanation

Mechanics of Materials

43 Questions

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q15

NAT[1 Mark]

A steel plate having yield strength of $550~MPa$, is subjected to biaxial state of stress as $\sigma_{x}=\sigma$ and $\sigma_{y}=-2\sigma$. Using distortion energy theory and considering the factor of safety as 2, the permissible value of $\sigma$ that can be applied to the plate is ____ MPa (rounded off to 1 decimal place).

Explanation

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q16

MCQ[2 Marks]

A cantilever beam of length L is subjected to a concentrated load P and a moment M as shown in the figure below. Neglecting the mass of the beam, which one of the following options is the correct representation of shear force diagram (SFD) and bending moment diagram (BMD)?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q17

NAT[2 Marks]

A simply supported beam is subjected to an external point load $P$ as shown in the figure below. The beam has a rectangular cross-section of $20~mm \times 45~mm$. A is a pin support and B is a roller support. The shear stress developed at point C, lying on the neutral axis of the beam, is $3~MPa$. Neglecting the mass of the beam, the magnitude of the applied load is ____ kN (rounded off to 1 decimal place).

Explanation

GATE→2026→Applied Mechanics and Design→Mechanics of Materials

Q18

NAT[2 Marks]

A cylindrical pressure vessel made of steel has diameter of $3~m$ and wall thickness of $15~mm$. For steel, Young's modulus and Poisson's ratio are $210~GPa$ and $0.3$, respectively. The cylinder is designed such that the allowable normal strain at the outer cylindrical surface is equal to $0.00034$. The permissible pressure in the tank is ____ kPa (rounded off to 1 decimal place).

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q19

MCQ[1 Mark]

The yield stress of a metal in uniaxial tension is $200~MPa$. According to von Mises yield criterion, the yield stress (in MPa) of the metal in pure shear is closest to

(A)

115.5

(B)

100.0

(C)

66.7

(D)

141.4

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q20

MCQ[1 Mark]

A metallic square plate is subjected to a uniform hydrostatic pressure (P). Choose the correct Mohr's circle representing the state of stress at any point in the plate from the options given below.\nFor the Mohr's circle, normal stress is positive towards right and shear stress is positive in the upward direction.

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q21

NAT[2 Marks]

The state of stress at a point is shown in the figure given below. Under plane stress assumption, the normal strain along the thickness direction $(\epsilon_{zz})$ is ____ (rounded off to 2 decimal places).\nUse the Young's Modulus $E=200~GPa$ and Poisson's ratio $\nu=0.27$.

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q22

NAT[2 Marks]

A simply supported beam of length $1~m$ is subjected to a uniformly distributed bending moment of $1~N~m$ per $m$ throughout the length as shown in the figure given below. The bending moment at the mid-point of the beam is ____ N m (rounded off to the nearest integer).

Explanation

GATE→2025→Applied Mechanics and Design→Mechanics of Materials

Q23

NAT[2 Marks]

An isotropic brittle material is tested in the universal testing machine. The stress-strain diagram for the material shows a bi-linear elastic behavior as shown in the figure given below. The strain energy density is ____ MJ $m^{-3}$ (rounded off to 2 decimal places).

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q24

MCQ[1 Mark]

The effective stiffness of a cantilever beam of length L and flexural rigidity EI subjected to a transverse tip load W is

(A)

\frac{3EI}{L^{3}}

(B)

\frac{2EI}{L^{3}}

(C)

\frac{L^{3}}{2EI}

(D)

\frac{L^{3}}{3EI}

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q25

MSQ[1 Mark]

A beam is undergoing pure bending as shown in the figure. The stress ($\sigma$)-strain ($\varepsilon$) curve for the material is also given. The yield stress of the material is $\sigma_{Y}$. Which of the option(s) given represent(s) the bending stress distribution at cross-section AA after plastic yielding?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q26

MSQ[1 Mark]

The principal stresses at a point P in a solid are $70~MPa$, $-70~MPa$ and $0$. The yield stress of the material is $100~MPa$. Which prediction(s) about material failure at P is/are CORRECT?

(A)

Maximum normal stress theory predicts material fails

(B)

Maximum shear stress theory predicts material fails

(C)

Maximum normal stress theory predicts material does not fail

(D)

Maximum shear stress theory predicts material does not fail

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q27

MSQ[1 Mark]

Which of the plot(s) shown is/are valid Mohr's circle representations of a plane stress state in a material? (The center of each circle is indicated by O.)

(A)

M1

(B)

M2

(C)

M3

(D)

M4

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q28

MCQ[2 Marks]

A beam of length L is loaded in the xy-plane by a uniformly distributed load, and by a concentrated tip load parallel to the z-axis, as shown in the figure. The resulting bending moment distributions about the y and the z axes are denoted by $M_{y}$ and $M_{z}$ respectively.\nWhich one of the options given depicts qualitatively CORRECT variations of $M_{y}$ and $M_{z}$ along the length of the beam?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q29

MCQ[2 Marks]

The figure shows a thin-walled open-top cylindrical vessel of radius $r$ and wall thickness $t$. The vessel is held along the brim and contains a constant-density liquid to height $h$ from the base. Neglect atmospheric pressure, the weight of the vessel and bending stresses in the vessel walls.\nWhich one of the plots depicts qualitatively CORRECT dependence of the magnitudes of axial wall stress $(\sigma_{1})$ and circumferential wall stress $(\sigma_{2})$ on y?

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q30

MSQ[2 Marks]

Cylindrical bars P and Q have identical lengths and radii, but are composed of different linear elastic materials. The Young's modulus and coefficient of thermal expansion of Q are twice the corresponding values of P. Assume the bars to be perfectly bonded at the interface, and their weights to be negligible.\nThe bars are held between rigid supports as shown in the figure and the temperature is raised by $\Delta T$. Assume that the stress in each bar is homogeneous and uniaxial. Denote the magnitudes of stress in P and Q by $\sigma_{1}, \sigma_{2}$, respectively.\nWhich of the statement(s) given is/are CORRECT?

(A)

The interface between P and Q moves to the left after heating

(B)

The interface between P and Q moves to the right after heating

(C)

\sigma_{1} < \sigma_{2}

(D)

\sigma_{1} = \sigma_{2}

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q31

NAT[2 Marks]

An optical flat is used to measure the height difference between a reference slip gauge A and a slip gauge B. Upon viewing via the optical flat using a monochromatic light of wavelength $0.5~\mu m$, $12$ fringes were observed over a length of $15~mm$ of gauge B. If the gauges are placed $45~mm$ apart, the height difference of the gauges is ____ \mu m. (Answer in integer)

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q32

NAT[2 Marks]

Ignoring the small elastic region, the true stress ($\sigma$) - true strain ($\varepsilon$) variation of a material beyond yielding follows the equation $\sigma = 400\varepsilon^{0.3}~MPa$. The engineering ultimate tensile strength value of this material is ____ MPa.

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q33

NAT[2 Marks]

The area moment of inertia about the y-axis of a linearly tapered section shown in the figure is ____ $m^{4}$ (Answer in integer)

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q34

NAT[2 Marks]

A cylindrical bar has a length $L=5~m$ and cross section area $S=10~m^{2}$. The bar is made of a linear elastic material with a density $\rho=2700~kg/m^{3}$ and Young's modulus $E=70~GPa$. The bar is suspended as shown in the figure and is in a state of uniaxial tension due to its self-weight.\nThe elastic strain energy stored in the bar equals ____ J. (Rounded off to two decimal places)\nTake the acceleration due to gravity as $g=9.8~m/s^{2}$.

Explanation

GATE→2023→Applied Mechanics and Design→Mechanics of Materials

Q35

NAT[2 Marks]

A cylindrical transmission shaft of length $1.5~m$ and diameter $100~mm$ is made of a linear elastic material with a shear modulus of $80~GPa$. While operating at $500~rpm$, the angle of twist across its length is found to be $0.5~degrees$.\nThe power transmitted by the shaft at this speed is ____ kW. (Rounded off to two decimal places)\nTake $\pi=3.14$.

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q36

MCQ[1 Mark]

A uniform light slender beam AB of section modulus 𝐸𝐼 is pinned by a frictionless joint A to the ground and supported by a light inextensible cable CB to hang a weight 𝑊 as shown. If the maximum value of 𝑊 to avoid buckling of the beam AB is obtained as 𝛽𝜋ଶ𝐸𝐼, where 𝜋 is the ratio of circumference to diameter of a circle, then the value of 𝛽 is (A) 0.0924 m-2 (B) 0.0713 m-2 (C) 0.1261 m-2 (D) 0.1417 m-2 2.5 m 30° 𝑊 𝑔 C B A

(A)

0.0924 m-2

(B)

0.0713 m-2

(C)

0.1261 m-2

(D)

0.1417 m-2 2.5 m 30° 𝑊 𝑔 C B A

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q37

MCQ[1 Mark]

The figure shows a schematic of a simple Watt governor mechanism with the spindle O1O2 rotating at an angular velocity ω about a vertical axis. The balls at P and S have equal mass. Assume that there is no friction anywhere and all other components are massless and rigid. The vertical distance between the horizontal plane of rotation of the balls and the pivot O1 is denoted by h. The value of h = 400 mm at a certain ω. If ω is doubled, the value of h will be _________ mm. (A) 50 (B) 100 (C) 150 (D) 200

(A)

50

(B)

100

(C)

150

(D)

200

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q38

MCQ[1 Mark]

A square threaded screw is used to lift a load W by applying a force F. Efficiency of square threaded screw is expressed as (A) The ratio of work done by W per revolution to work done by F per revolution (B) 𝑾/𝑭 (C) 𝑭/𝑾 (D) The ratio of work done by F per revolution to work done by W per revolution

(A)

The ratio of work done by W per revolution to work done by F per revolution

(B)

𝑾/𝑭

(C)

𝑭/𝑾

(D)

The ratio of work done by F per revolution to work done by W per revolution

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q39

MCQ[1 Mark]

A CNC worktable is driven in a linear direction by a lead screw connected directly to a stepper motor. The pitch of the lead screw is 5 mm. The stepper motor completes one full revolution upon receiving 600 pulses. If the worktable speed is 5 m/minute and there is no missed pulse, then the pulse rate being received by the stepper motor is (A) 20 kHz (B) 10 kHz (C) 3 kHz (D) 15 kHz

(A)

20 kHz

(B)

10 kHz

(C)

3 kHz

(D)

15 kHz

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q40

MCQ[1 Mark]

The type of fit between a mating shaft of diameter 25.0 ା଴.଴ଵ଴ ି଴.଴ଵ଴ mm and a hole of diameter 25.015 ା ଴.଴ଵହ ି଴.଴ଵହ mm is __________. (A) Clearance (B) Transition (C) Interference (D) Linear

(A)

Clearance

(B)

Transition

(C)

Interference

(D)

Linear

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q41

MSQ[1 Mark]

Assuming the material considered in each statement is homogeneous, isotropic, linear elastic, and the deformations are in the elastic range, which one or more of the following statement(s) is/are TRUE? (A) A body subjected to hydrostatic pressure has no shear stress. (B) If a long solid steel rod is subjected to tensile load, then its volume increases. (C) Maximum shear stress theory is suitable for failure analysis of brittle materials. (D) If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.

(A)

A body subjected to hydrostatic pressure has no shear stress.

(B)

If a long solid steel rod is subjected to tensile load, then its volume increases.

(C)

Maximum shear stress theory is suitable for failure analysis of brittle materials.

(D)

If a portion of a beam has zero shear force, then the corresponding portion of the elastic curve of the beam is always straight.

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q42

MSQ[1 Mark]

Which of the following methods can improve the fatigue strength of a circular mild steel (MS) shaft? (A) Enhancing surface finish (B) Shot peening of the shaft (C) Increasing relative humidity (D) Reducing relative humidity

(A)

Enhancing surface finish

(B)

Shot peening of the shaft

(C)

Increasing relative humidity

(D)

Reducing relative humidity

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q43

NAT[1 Mark]

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∙cm2 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). O 200 cm/s 10 cm

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q44

NAT[1 Mark]

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 = 5.669  10-8 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).

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q45

MCQ[2 Marks]

An L-shaped elastic member ABC with slender arms AB and BC of uniform cross- section is clamped at end A and connected to a pin at end C. The pin remains in continuous contact with and is constrained to move in a smooth horizontal slot. The section modulus of the member is same in both the arms. The end C is subjected to a horizontal force 𝑃 and all the deflections are in the plane of the figure. Given the length AB is 4𝑎 and length BC is 𝑎, the magnitude and direction of the normal force on the pin from the slot, respectively, are (A) 3𝑃/8, and downwards (B) 5𝑃/8, and upwards (C) 𝑃/4, and downwards (D) 3𝑃/4, and upwards A B C 4a P a

(A)

3𝑃/8, and downwards

(B)

5𝑃/8, and upwards

(C)

𝑃/4, and downwards

(D)

3𝑃/4, and upwards A B C 4a P a

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q46

MCQ[2 Marks]

A planar four-bar linkage mechanism with 3 revolute kinematic pairs and 1 prismatic kinematic pair is shown in the figure, where AB ⊥ CE and FD ⊥ CE. The T-shaped link CDEF is constructed such that the slider B can cross the point D, and CE is sufficiently long. For the given lengths as shown, the mechanism is (A) a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG (B) a non-Grashof chain with all oscillating links (C) a Grashof chain with AB completely rotatable about the ground link FG, and oscillatory links AG and CDEF (D) on the border of Grashof and non-Grashof chains with uncertain configuration(s) G A B D C F 5 cm 3 cm 1.5 cm 3 cm E

(A)

a Grashof chain with links AG, AB, and CDEF completely rotatable about the ground link FG

(B)

a non-Grashof chain with all oscillating links

(C)

a Grashof chain with AB completely rotatable about the ground link FG, and oscillatory links AG and CDEF

(D)

on the border of Grashof and non-Grashof chains with uncertain configuration(s) G A B D C F 5 cm 3 cm 1.5 cm 3 cm E

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q47

MCQ[2 Marks]

Consider a forced single degree-of-freedom system governed by 𝑥̈(𝑡) + 2ζ𝜔௡𝑥̇(𝑡) + 𝜔௡ ଶ𝑥(𝑡) = 𝜔௡ ଶcos(𝜔𝑡), where ζ and 𝜔௡ are the damping ratio and undamped natural frequency of the system, respectively, while 𝜔 is the forcing frequency. The amplitude of the forced steady state response of this system is given by [(1 −𝑟ଶ)ଶ+ (2ζ𝑟)ଶ]ିଵ/ଶ, where 𝑟= 𝜔/𝜔௡. The peak amplitude of this response occurs at a frequency 𝜔= 𝜔௣. If 𝜔ௗ denotes the damped natural frequency of this system, which one of the following options is true? (A) 𝜔௣< 𝜔ௗ< 𝜔௡ (B) 𝜔௣= 𝜔ௗ< 𝜔௡ (C) 𝜔ௗ< 𝜔௡= 𝜔௣ (D) 𝜔ௗ< 𝜔௡< 𝜔௣

(A)

𝜔௣< 𝜔ௗ< 𝜔௡

(B)

𝜔௣= 𝜔ௗ< 𝜔௡

(C)

𝜔ௗ< 𝜔௡= 𝜔௣

(D)

𝜔ௗ< 𝜔௡< 𝜔௣

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q48

MCQ[2 Marks]

A bracket is attached to a vertical column by means of two identical rivets U and V separated by a distance of 2a = 100 mm, as shown in the figure. The permissible shear stress of the rivet material is 50 MPa. If a load P = 10 kN is applied at an eccentricity 𝑒= 3√7 𝑎, the minimum cross-sectional area of each of the rivets to avoid failure is ___________ mm2. (A) 800 (B) 25 (C) 100√7 (D) 200

(A)

800

(B)

25

(C)

100√7

(D)

200

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q49

MCQ[2 Marks]

Consider a rod of uniform thermal conductivity whose one end (𝑥= 0) is insulated and the other end (𝑥= 𝐿) is exposed to flow of air at temperature T∞ with convective heat transfer coefficient h. The cylindrical surface of the rod is insulated so that the heat transfer is strictly along the axis of the rod. The rate of internal heat generation per unit volume inside the rod is given as 𝑞̇ = cos 2𝜋𝑥 𝐿 . The steady state temperature at the mid-location of the rod is given as TA. What will be the temperature at the same location, if the convective heat transfer coefficient increases to 2h? (A) 𝑇஺+ 𝑞̇𝐿 2ℎ (B) 2𝑇஺ (C) 𝑇஺ (D) 𝑇஺൬1 −𝑞̇𝐿 4𝜋ℎ൰+ 𝑞̇𝐿 4𝜋ℎ𝑇ஶ

(A)

𝑇஺+ 𝑞̇𝐿 2ℎ

(B)

2𝑇஺

(C)

𝑇஺

(D)

𝑇஺൬1 −𝑞̇𝐿 4𝜋ℎ൰+ 𝑞̇𝐿 4𝜋ℎ𝑇ஶ

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q50

NAT[2 Marks]

A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. AE is a single member that contains pin C. Likewise, BE is a single member that contains pin D. Members GI and FH are overlapping rigid members. The magnitude of the force carried by member CI is ________ kN (in integer). 2m 2m 3m 3m 3m 3.5 m 3m A B C D E I H F G 2 kN 4 kN

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q51

NAT[2 Marks]

Two rigid massless rods PR and RQ are joined at frictionless pin-joint R and are resting on ground at P and Q, respectively, as shown in the figure. A vertical force F acts on the pin R as shown. When the included angle 𝜃< 90°, the rods remain in static equilibrium due to Coulomb friction between the rods and ground at locations P and Q. At 𝜃= 90°, impending slip occurs simultaneously at points P and Q. Then the ratio of the coefficient of friction at Q to that at P (µQ /µP) is _________ (round off to two decimal places). P Q F 5 m 12 m R 𝜃

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q52

NAT[2 Marks]

A cylindrical disc of mass 𝑚= 1 kg and radius 𝑟= 0.15 m was spinning at 𝜔= 5 rad/s when it was placed on a flat horizontal surface and released (refer to the figure). Gravity 𝑔 acts vertically downwards as shown in the figure. The coefficient of friction between the disc and the surface is finite and positive. Disregarding any other dissipation except that due to friction between the disc and the surface, the horizontal velocity of the center of the disc, when it starts rolling without slipping, will be _________ m/s (round off to 2 decimal places).

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q53

NAT[2 Marks]

A thin-walled cylindrical pressure vessel has mean wall thickness of 𝑡 and nominal radius of 𝑟. The Poisson’s ratio of the wall material is 1/3. When it was subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by 0.1% and the corresponding wall thickness became 𝑡̅. The corresponding change in the wall thickness of the cylindrical portion, i.e. 100 × (𝑡̅ −𝑡)/𝑡, is ________% (round off to 3 decimal places). 𝜔 𝑟 𝑚 𝑔

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q54

NAT[2 Marks]

A schematic of an epicyclic gear train is shown in the figure. The sun (gear 1) and planet (gear 2) are external, and the ring gear (gear 3) is internal. Gear 1, gear 3 and arm OP are pivoted to the ground at O. Gear 2 is carried on the arm OP via the pivot joint at P, and is in mesh with the other two gears. Gear 2 has 20 teeth and gear 3 has 80 teeth. If gear 1 is kept fixed at 0 rpm and gear 3 rotates at 900 rpm counter clockwise (ccw), the magnitude of angular velocity of arm OP is __________rpm (in integer).

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q55

NAT[2 Marks]

Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of 4 m/s. The orthogonal rake angle of the cutting tool is 5º. The uncut chip thickness and width of cut are 0.2 mm and 3 mm, respectively. In this turning operation, the resulting friction angle and shear angle are 45º and 25º, respectively. If the dynamic yield shear strength of the workpiece material under this cutting condition is 1000 MPa, then the cutting force is ______________ N (round off to one decimal place).

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q56

NAT[2 Marks]

A 4 mm thick aluminum sheet of width w = 100 mm is rolled in a two-roll mill of roll diameter 200 mm each. The workpiece is lubricated with a mineral oil, which gives a coefficient of friction, µ = 0.1. The flow stress (𝜎 ) of the material in MPa is 𝜎 = 207 + 414 𝜀, where 𝜀 is the true strain. Assuming rolling to be a plane strain deformation process, the roll separation force (F) for maximum permissible draft (thickness reduction) is _________ kN (round off to the nearest integer). Use: 𝐹= 1.15 𝜎ത ቀ1 + µ௅ ଶ௛ഥቁ 𝑤𝐿, where 𝜎ത is average flow stress, 𝐿 is roll-workpiece contact length, and ℎത is the average sheet thickness.

Explanation

GATE→2022→Applied Mechanics and Design→Mechanics of Materials

Q57

NAT[2 Marks]

The product structure diagram shows the number of different components required at each level to produce one unit of the final product P. If there are 50 units of on- hand inventory of component A, the number of additional units of component A needed to produce 10 units of product P is _________ (in integer).

Explanation

Theory of Machines

9 Questions

GATE→2026→Applied Mechanics and Design→Theory of Machines

Q58

MCQ[1 Mark]

A gear train with five gears is shown in the figure below. The number of teeth on each gear is $N_{1}$, $N_{2}$, $N_{3}$, $N_{4}$, and $N_{5}$. The idler gear in this gear train is

(A)

gear 4

(B)

gear 2

(C)

gear 3

(D)

gear 1

Explanation

GATE→2026→Applied Mechanics and Design→Theory of Machines

Q59

MCQ[1 Mark]

The rotor of an aeroplane engine has a mass moment of inertia $1.0~kg~m^{2}$. The engine rotates at a speed of 500 RPM in the clockwise direction if viewed from the front of the aeroplane. If the aeroplane while flying at $1200~km/hr$ turns with a radius of $2~km$ at same elevation, then the magnitude of the gyroscopic moment exerted by the rotor on the aeroplane structure in $N~m$ is

(A)

8.73

(B)

17.46

(C)

4.37

(D)

26.19

Explanation

GATE→2025→Applied Mechanics and Design→Theory of Machines

Q60

MCQ[1 Mark]

In the context of balancing of rotating and reciprocating masses, which one of the following options is true?

(A)

An unbalanced rigid rotor can be completely balanced using a single balancing mass

(B)

An unbalanced rigid rotor can be completely balanced using two balancing masses attached in two distinct planes

(C)

A single-cylinder internal combustion engine can be completely balanced using a single balancing mass

(D)

A single-cylinder internal combustion engine can be completely balanced using two balancing masses

Explanation

GATE→2025→Applied Mechanics and Design→Theory of Machines

Q61

NAT[2 Marks]

A pair of spur gears is required to maintain a velocity ratio of $1:2$. The module of the gears is $10~mm$ and the addendum is $10~mm$. If the operating pressure angle is $15^{\circ}$, the minimum number of teeth required on the pinion to ensure NO interference/undercutting is ____ (answer in integer).

Explanation

GATE→2025→Applied Mechanics and Design→Theory of Machines

Q62

NAT[2 Marks]

An offset slider-crank mechanism is shown in the figure below. The length of the stroke of the slider is ____ mm (rounded off to nearest integer).

Explanation

GATE→2024→Applied Mechanics and Design→Theory of Machines

Q63

MCQ[1 Mark]

The change in kinetic energy $\Delta E$ of an engine is $300~J$, and minimum and maximum shaft speeds are $\omega_{min}=220~rad/s$ and $\omega_{max}=280~rad/s$, respectively. Assume that the torque-time function is purely harmonic. To achieve a coefficient of fluctuation of $0.05$, the moment of inertia (in $kg \cdot m^{2}$) of the flywheel to be mounted on the engine shaft is

(A)

0.15

(B)

0.31

(C)

0.24

(D)

0.053

Explanation

GATE→2024→Applied Mechanics and Design→Theory of Machines

Q64

NAT[2 Marks]

The Levai type-A train illustrated in the figure has gears with module $m=8~mm/tooth$. Gears 2 and 3 have 19 and 24 teeth respectively. Gear 2 is fixed and internal gear 4 rotates at $20~rev/min$ counter-clockwise. The magnitude of angular velocity of the arm is ____ rev/min. (rounded off to 2 decimal places)

Explanation

GATE→2024→Applied Mechanics and Design→Theory of Machines

Q65

NAT[2 Marks]

At the instant when OP is vertical and AP is horizontal, the link OD is rotating counter clockwise at a constant rate $\omega=7~rad/s$. Pin P on link OD slides in the slot BC of link ABC which is hinged at A, and causes a clockwise rotation of the link ABC. The magnitude of angular velocity of link ABC for this instant is ____ rad/s (rounded off to 2 decimal places).

Explanation

GATE→2023→Applied Mechanics and Design→Theory of Machines

Q66

NAT[1 Mark]

Two meshing spur gears 1 and 2 with diametral pitch of $8~teeth/mm$ and an angular velocity ratio $|\omega_{2}|/|\omega_{1}|=1/4$ have their centers $30~mm$ apart. The number of teeth on the driver (gear 1) is

Explanation

Vibrations

7 Questions

GATE→2026→Applied Mechanics and Design→Vibrations

Q67

MCQ[1 Mark]

In a single degree of freedom vibrating system with only viscous damping, the critical damping coefficient is $350~N~s/m$ and the damping coefficient is $35~N~s/m$. The logarithmic decrement of the vibrating system is

(A)

0.63

(B)

1.26

(C)

0.32

(D)

1.89

Explanation

GATE→2026→Applied Mechanics and Design→Vibrations

Q68

MCQ[2 Marks]

A 5 kg mass is suspended at the free end of an overhanging massless beam, having a pin support and a roller support, as shown in the figure below. Young's modulus of the material of the beam is 200 GPa and area moment of inertia of the beam is $10^{-8}~m^{4}$. The natural frequency of the beam in rad/s is

(A)

10

(B)

10/3

(C)

5

(D)

20/3

Explanation

GATE→2025→Applied Mechanics and Design→Vibrations

Q69

NAT[1 Mark]

A block of mass $1~kg$ connected to a spring of stiffness $10~N~m^{-1}$ is operating in a viscous medium such that the damping ratio (or damping factor) is equal to the ratio of the damped frequency to the natural frequency. The magnitude of the damping ratio for this system is ____ (rounded off to 2 decimal places).

Explanation

GATE→2025→Applied Mechanics and Design→Vibrations

Q70

MCQ[2 Marks]

The system shown in the figure below consists of a cantilever beam (with flexural rigidity $EI$ and negligible mass), a spring (with spring constant $K$ and negligible mass) and a block of mass $m$. Assuming a lumped parameter model for the system, the fundamental natural frequency $(\omega_{n})$ of the system is

(A)

A

(B)

B

(C)

C

(D)

D

Explanation

GATE→2024→Applied Mechanics and Design→Vibrations

Q71

MCQ[1 Mark]

A linear spring-mass-dashpot system with a mass of $2~kg$ is set in motion with viscous damping. If the natural frequency is $15~Hz$, and the amplitudes of two successive cycles measured are $7.75~mm$ and $7.20~mm$, the coefficient of viscous damping (in $N \cdot s/m$) is

(A)

4.41

(B)

7.51

(C)

2.52

(D)

6.11

Explanation

GATE→2024→Applied Mechanics and Design→Vibrations

Q72

NAT[2 Marks]

A vibratory system consists of mass $m$, a vertical spring of stiffness $2k$ and a horizontal spring of stiffness $k$. The end A of the horizontal spring is given a horizontal motion $x_{A}=a \sin \omega t$. The other end of the spring is connected to an inextensible rope that passes over two massless pulleys as shown. Assume $m=10~kg$, $k=1.5~kN/m$ and neglect friction. The magnitude of critical driving frequency for which the oscillations of mass m tend to become excessively large is ____ rad/s (answer in integer).

Explanation

GATE→2023→Applied Mechanics and Design→Vibrations

Q73

NAT[1 Mark]

The figure shows a block of mass $m=20~kg$ attached to a pair of identical linear springs, each having a spring constant $k=1000~N/m$. The block oscillates on a frictionless horizontal surface. Assuming free vibrations, the time taken by the block to complete ten oscillations is ____ seconds. (Rounded off to two decimal places)\nTake $\pi=3.14$.

Explanation

Machine Design

14 Questions

GATE→2026→Applied Mechanics and Design→Machine Design

Q74

MCQ[1 Mark]

A closely coiled helical compression spring of mean coil diameter $D$ and wire diameter $d$, is loaded by an axial force $F$. The maximum shear stress developed in the wire is

(A)

\frac{8FD}{\pi d^{3}}+\frac{4F}{\pi d^{2}}

(B)

\frac{8FD}{\pi d^{3}}+\frac{2F}{\pi d^{2}}

(C)

\frac{16FD}{\pi d^{3}}+\frac{4F}{\pi d^{2}}

(D)

\frac{32FD}{\pi d^{3}}+\frac{4F}{\pi d^{2}}

Explanation

GATE→2026→Applied Mechanics and Design→Machine Design

Q75

MCQ[1 Mark]

A rectangular plate is perfectly welded to a gusset plate with parallel fillet weld joints as shown in the figure below. The length of the weld is $l$ and the fillet weld leg size is $h$. The allowable shear strength of the weldment is $\tau_{all}$. A tensile force $P$ is applied on the plate in a direction parallel to the length of the weld. Assuming the throat of the weld as the weakest section, the critical load is

(A)

\sqrt{2}hl\tau_{all}

(B)

hl\tau_{all}

(C)

hl\tau_{all}/\sqrt{2}

(D)

hl\tau_{all}/2

Explanation

GATE→2026→Applied Mechanics and Design→Machine Design

Q76

MCQ[1 Mark]

Worm gearsets are used for transmitting rotary motion between

(A)

non-parallel and non-intersecting shafts

(B)

intersecting shafts

(C)

parallel shafts

(D)

non-parallel and intersecting shafts

Explanation

GATE→2026→Applied Mechanics and Design→Machine Design

Q77

NAT[2 Marks]

A welded square plate of $1~m \times 1~m$ is subjected to biaxial stress of magnitude $6.5~MPa$ and $25~MPa$, as shown in the figure below. The ratio of the normal stress acting in the perpendicular direction of सरपंच the weld to the shear stress of the weld is ____ (rounded off to 2 decimal places).

Explanation

GATE→2025→Applied Mechanics and Design→Machine Design

Q78

MCQ[1 Mark]

A shaft carries a helical spur gear. Which one of the following bearings can NOT be used to support it?

(A)

Angular contact bearing

(B)

Double-row ball bearing

(C)

Straight roller bearing

(D)

Tapered roller bearing

Explanation

GATE→2025→Applied Mechanics and Design→Machine Design

Q79

MCQ[2 Marks]

The endurance limit of a specific grade of steel is same as its yield strength. The ultimate strength of this grade of steel is twice of its yield strength. A component made of this steel is loaded in tension and unloaded periodically. It is required that the component does NOT fail for at least $10^{6}$ loading cycles, as per the Soderberg law. Considering a factor of safety of 2, the maximum applied tensile principal stress is

(A)

one-fourth of endurance limit

(B)

half of endurance limit

(C)

the endurance limit

(D)

twice the endurance limit

Explanation

GATE→2025→Applied Mechanics and Design→Machine Design

Q80

NAT[2 Marks]

Two plates of thickness $10~mm$ each are to be joined by a transverse fillet weld on one side and the resulting structure is loaded as shown in the figure below. If the ultimate tensile strength of the weld material is $150~MPa$ and the factor of safety to be used is $3$, the minimum length of the weld required to ensure that the weld does NOT fail is ____ mm (rounded off to 2 decimal places).

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q81

MCQ[1 Mark]

For a ball bearing, the fatigue life in millions of revolutions is given by $$L=\left(\frac{C}{P}\right)^{n}$$\nwhere $P$ is the constant applied load and $C$ is the basic dynamic load rating. Which one of the following statements is TRUE?

(A)

n = 3 assuming inner racing fixed and outer revolving

(B)

n = 1/3 assuming inner racing fixed and outer revolving

(C)

n = 3 assuming outer racing is fixed

(D)

n = 1/3 assuming outer racing is fixed

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q82

MCQ[1 Mark]

Which one of the following failure theories is the most conservative design approach against fatigue failure?

(A)

Soderberg line

(B)

Modified Goodman line

(C)

Gerber line

(D)

Yield line

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q83

NAT[2 Marks]

A solid massless cylindrical member of $50~mm$ diameter is rigidly attached at one end, and is subjected to an axial force $P=100~KN$ and a torque $T=600~N \cdot m$ at the other end as shown. Assume that the axis of the cylinder is normal to the support. Considering distortion energy theory with allowable yield stress as $300~MPa$, the factor of safety in the design is ____ (rounded off to 1 decimal place).

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q84

NAT[2 Marks]

The figure shows a thin cylindrical pressure vessel constructed by welding plates together along a line that makes an angle $\alpha=60^{\circ}$ with the horizontal. The closed vessel has a wall thickness of $10~mm$ and diameter of $2~m$. When subjected to an internal pressure of $200~kPa$, the magnitude of the normal stress acting on the weld is ____ MPa (rounded off to 1 decimal place).

Explanation

GATE→2024→Applied Mechanics and Design→Machine Design

Q85

NAT[2 Marks]

A band brake shown in the figure has a coefficient of friction of $0.3$. The band can take a maximum force of $1.5~kN$. The maximum braking force ($F$) that can be safely applied is ____ N (rounded off to the nearest integer).

Explanation

GATE→2023→Applied Mechanics and Design→Machine Design

Q86

MCQ[1 Mark]

The S-N curve from a fatigue test for steel is shown. Which one of the options gives the endurance limit?

(A)

S_{ut}

(B)

S_{2}

(C)

S_{3}

(D)

S_{4}

Explanation

GATE→2023→Applied Mechanics and Design→Machine Design

Q87

NAT[1 Mark]

The braking system shown in the figure uses a belt to slow down a pulley rotating in the clockwise direction by the application of a force P. The belt wraps around the pulley over an angle $\alpha=270$ degrees. The coefficient of friction between the belt and the pulley is $0.3$. The influence of centrifugal forces on the belt is negligible.\nDuring braking, the ratio of the tensions $T_{1}$ to $T_{2}$ in the belt is equal to ____ (Rounded off to two decimal places)\nTake $\pi=3.14$.

Explanation