Hot questions in Applied Mechanics and Design / GO Mechanical

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GATE2016-1-37
A solid disc with radius $a$ is connected to a spring at a point $d$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $M$ and the spring constant is $K$. The ... $\displaystyle{\sqrt{\frac{2K(a+d)^2}{Ma^2}}} \\$ $\displaystyle{\sqrt{\frac{K(a+d)^2}{Ma^2}}}$

A solid disc with radius $a$ is connected to a spring at a point $d$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is ...

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GATE Mechanical 2014 Set 1 | Question: 25
In solid-state welding, the contamination layers between the surfaces to be welded are removed by alcohol plastic deformation water jet sand blasting

In solid-state welding, the contamination layers between the surfaces to be welded are removed byalcoholplastic deformationwater jetsand blasting

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GATE2017 ME-1: 42
A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3), S(0, 3)$ ... . The deformed length of the elongated diagonal, up to three decimal places is _______ units.

A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3)...

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GATE2015-2-31
A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of $10$ $kN$ is applied at the mid-point of PQ. The magnitude of bending moment (in $kN$-$m$) at fixed end O is $2.5$ $5$ $10$ $25$

A cantilever beam OP is connected to another beam PQ with a pin joint as shown in the figure. A load of $10$ $kN$ is applied at the mid-point of PQ. The magnitude of bend...

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GATE2017 ME-1: 48
A $10$ mm deep cylindrical cup with diameter of $15$ mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto $2$ decimal points accuracy) of the blank is _________ mm.

A $10$ mm deep cylindrical cup with diameter of $15$ mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto $2$ decimal po...

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GATE2017 ME-1: 39
An initially stress-free massless elastic beam of length $L$ and circular cross-section with diameter $d$ $(d << L)$ is held fixed between two walls as shown. The beam material has Young's modulus $E$ and coefficient of thermal expansion $a$. If the beam is ... , the temperature rise required to cause the beam to buckle is proportional to $d$ $d^{2}$ $d^{3}$ $d^{4}$

An initially stress-free massless elastic beam of length $L$ and circular cross-section with diameter $d$ $(d << L)$ is held fixed between two walls as shown. The beam ma...

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GATE2017 ME-1: 43
A machine element has an ultimate strength $(\sigma _{u})$ of $600 N/mm^{2}$, and endurance limit $(\sigma _{en})$ of $250 N/mm^{2}$. The fatigue curve for the element on a $\log-\log$ plot is shown below. If the element is to be designed for a finite life of $10000$ cycles, the maximum amplitude of a completely reversed operating stress is _________ $N/mm^{2}$.

A machine element has an ultimate strength $(\sigma _{u})$ of $600 N/mm^{2}$, and endurance limit $(\sigma _{en})$ of $250 N/mm^{2}$. The fatigue curve for the element on...

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GATE2016-3-33
A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus $E=200 \: GPa$ .The deformed shape is a square of dimension $L− 2\delta$. If $L = 2 \: m$ and $\delta=0.001 \: m$, the Poisson’s ratio of the plate material is __________

A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Y...

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GATE2016-2-37
The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. The spring constant $k$ is $1500$ $N/m$. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ $rad/s$.

The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. ...

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GATE2017 ME-2: 33
A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wire is $24$MPa. For the same compressive load, if both the wire diameter and the mean coil diameter are doubled, the maximum shear stress (in MPa) induced in the cross-section of the wire is __________.

A helical compression spring made of a wire of circular cross-section is subjected to a compressive load. The maximum shear stress induced in the cross-section of the wir...

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GATE2017 ME-2: 31
The radius of gyration of a compound pendulum about the point of suspension is $100$ mm. The distance between the point of suspension and the centre of mass is $250$ mm. Considering the acceleration due to gravity as $9.81 m/s^{2}$, the natural frequency (in radian/s) of the compound pendulum is ________.

The radius of gyration of a compound pendulum about the point of suspension is $100$ mm. The distance between the point of suspension and the centre of mass is $250$ mm. ...

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GATE2017 ME-1: 40
A point mass of $100$ kg is dropped onto a massless elastic bar (cross-sectional area $= 100 mm^{2}$, length $= 1$ m, Young's modulus$=100$ GPa) from a height $H$ of $10$ mm as shown (Figure is not to scale). If $g= 10 m/s^{2}$, the maximum compression of the elastic bar is _______ mm

A point mass of $100$ kg is dropped onto a massless elastic bar (cross-sectional area $= 100 mm^{2}$, length $= 1$ m, Young's modulus$=100$ GPa) from a height $H$ of $10$...

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GATE2016-1-48
A hypothetical engineering stress-strain curve shown in the figure has three straight lines $PQ, QR, RS$ with coordinates P$(0,0)$, Q$(0.2,100)$, R$(0.6,140)$ and S$(0.8,130)$. $'Q'$ is the yield point, $'R'$ is the UTS point and $'S'$ the fracture point. The toughness of the material (in $MJ/m^3$) is __________

A hypothetical engineering stress-strain curve shown in the figure has three straight lines $PQ, QR, RS$ with coordinates P$(0,0)$, Q$(0.2,100)$, R$(0.6,140)$ and S$(0.8,...

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GATE2015-1-14
Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $\tau$ is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, $\theta$ versus time

Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $\tau$ is applied on the crank as shown in the figure. Which of the following plots b...

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GATE2017 ME-1: 47
For an inline slider-crank mechanism, the lengths of the crank and connecting rod are $3$ m and $4$ m, respectively. At the instant when the connecting rod is perpendicular to the crank, if the velocity of the slider is $1$ m/s, the magnitude of angular velocity (upto $3$ decimal points accuracy) of the crank is ________ radian/s

For an inline slider-crank mechanism, the lengths of the crank and connecting rod are $3$ m and $4$ m, respectively. At the instant when the connecting rod is perpendicul...

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GATE2017 ME-2: 37
The principal stresses at a point in a critical section of a machine component are $\sigma _{1}=60$ MPa, $\sigma _{2}=5$ MPa and $\sigma _{3}=-40$ MPa. For the material of the component, the tensile yield strength is $\sigma _{y}=200$ MPa. According to the maximum shear stress theory, the factor of safety is $1.67$ $2.00$ $3.60$ $4.00$

The principal stresses at a point in a critical section of a machine component are $\sigma _{1}=60$ MPa, $\sigma _{2}=5$ MPa and $\sigma _{3}=-40$ MPa. For the material o...

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GATE2017 ME-1: 41
Two disks $A$ and $B$ with identical mass $(m)$ and radius $(R)$ are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk $A$ has all of its mass concentrated at the rim, while Disk $B$ has its mass uniformly distributed. At the bottom of the ... centre of disk $B$ is $\sqrt{\dfrac{3}{4}} \\$ $\sqrt{\dfrac{3}{2}} \\$ $1 \\$ $\sqrt{2}$

Two disks $A$ and $B$ with identical mass $(m)$ and radius $(R)$ are initially at rest. They roll down from the top of identical inclined planes without slipping. Disk $A...

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GATE2017 ME-2: 30
Block $2$ slides outward on link $1$ at a uniform velocity of $6$ m/s as shown in the figure. Link $1$ is rotating at a constant angular velocity of $20$ radian/s counterclockwise. The magnitude of the total acceleration (in $m/s^{2}$) of point $P$ of the block with respect to fixed point $O$ is __________.

Block $2$ slides outward on link $1$ at a uniform velocity of $6$ m/s as shown in the figure. Link $1$ is rotating at a constant angular velocity of $20$ radian/s counter...

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GATE2017 ME-2: 34
Three masses are connected to a rotating shaft supported on bearings $A$ and $B$ ... and for a shaft angular speed of $1000$ radian/s, the magnitude of the bearing reaction (in N) at location $B$ is ___________.

Three masses are connected to a rotating shaft supported on bearings $A$ and $B$ as shown in the figure. The system is in a space where the gravitational effect is absent...

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GATE2017 ME-2: 35
A steel plate, connected to a fixed channel using three identical bolts $A, B$ and $C$, carries a load of $6$ kN as shown in the figure. Considering the effect of direct load and moment, the magnitude of resultant shear force (in kN) on bolt $C$ is $13$ $15$ $17$ $30$

A steel plate, connected to a fixed channel using three identical bolts $A, B$ and $C$, carries a load of $6$ kN as shown in the figure. Considering the effect of direct ...

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GATE2017 ME-1: 44
A horizontal bar, fixed at one end $(x=0)$, has a length of $1$ m, and cross-sectional area of $100 mm^{2}$. Its elastic modulus varies along its length as given by $E(x)=100 e^{-x}$ GPa, where $x$ is the length coordinate (in m) along the axis of the bar. An axial tensile load of $10$ kN is applied at the free end $(x=1)$. The axial displacement of the free end is _________ mm

A horizontal bar, fixed at one end $(x=0)$, has a length of $1$ m, and cross-sectional area of $100 mm^{2}$. Its elastic modulus varies along its length as given by $E(x)...

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GATE2017 ME-2: 32
A gear train shown in the figure consists of gears $P, Q, R,$ and $S$. Gear $Q$ and gear $R$ are mounted on the same shaft. All the gears are mounted on parallel shafts and the number of teeth of $P, Q, R$ and $S$ are $24, 45, 30,$ and $80$, respectively. Gear $P$ is rotating at $400$ rpm. The speed (in rpm) of the gear $S$ is __________.

A gear train shown in the figure consists of gears $P, Q, R,$ and $S$. Gear $Q$ and gear $R$ are mounted on the same shaft. All the gears are mounted on parallel shafts a...

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GATE2017 ME-1: 45
In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at $100$ rpm. Let the number of teeth on the sun, planet and outer gears to be $50, 25$ and $100$, respectively. The ratio of magnitudes of angular velocity of the planet gear to the angular velocity of the carrier arm is ________.

In an epicyclic gear train, shown in the figure, the outer ring gear is fixed, while the sun gear rotates counterclockwise at $100$ rpm. Let the number of teeth on the su...

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GATE2017 ME-2: 12
In a slider-crank mechanism, the lengths of the crank and the connecting rod are $100$ mm and $160$ mm, respectively. The crank is rotating with an angular velocity of $10$ radian/s counter-clockwise. The magnitude of linear velocity (in m/s) of the piston at the instant corresponding to the configuration shown in the figure is ________.

In a slider-crank mechanism, the lengths of the crank and the connecting rod are $100$ mm and $160$ mm, respectively. The crank is rotating with an angular velocity of $1...

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GATE2015-1-19
Which one of the following is the most conservative fatigue failure criterion? Soderberg Modified Goodman ASME Elliptic Gerber

Which one of the following is the most conservative fatigue failure criterion?SoderbergModified GoodmanASME EllipticGerber

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GATE2017 ME-1: 15
A motor driving a solid circular steel shaft transmits $40$ kW of power at $500$ rpm. If the diameter of the shaft is $40$ mm, the maximum shear stress in the shaft is _____________MPa.

A motor driving a solid circular steel shaft transmits $40$ kW of power at $500$ rpm. If the diameter of the shaft is $40$ mm, the maximum shear stress in the shaft is __...

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GATE2017 ME-2: 38
The rod $PQ$ of length $L=\sqrt{2}$ m, and uniformly distributed mass of $M=10$ kg, is released from rest at the position shown in the figure. The ends slide along the frictionless faces $OP$ and $OQ$. Assume acceleration due to gravity, $g=10 m/s^{2}$. ... figure is $(ML^{2}/12)$. At this instant, the magnitude of angular acceleration (in radian/$s^{2}$) of the rod is __________.

The rod $PQ$ of length $L=\sqrt{2}$ m, and uniformly distributed mass of $M=10$ kg, is released from rest at the position shown in the figure. The ends slide along the fr...

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GATE2017 ME-2: 8
For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is $M(x)=5x^{2}+10x$, where $x$ is the distance (in mm) measured from the free end of the beam. The magnitude of shear force (in N) in the cross-section at $x=10$ mm is __________.

For a loaded cantilever beam of uniform cross-section, the bending moment (in N.mm) along the length is $M(x)=5x^{2}+10x$, where $x$ is the distance (in mm) measured from...

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GATE2017 ME-1: 14
A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $r(t)=t^{2}, \theta (t)=t$, where $t$ is time. The Kinetic energy of the particle at time $t=2$ is $4$ $12$ $16$ $24$

A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $r(t)=t^{2}, \theta (t)=t$, where $t$ is time. The Kinetic energy of the p...

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GATE2015-1-38
Considering massless rigid rod and small oscillations, the natural frequency (in $rad/s$) of vibration of the system shown in the figure is $\sqrt{\dfrac{400}{1}} \\$ $\sqrt{\dfrac{400}{2}} \\$ $\sqrt{\dfrac{400}{3}} \\$ $\sqrt{\dfrac{400}{4}} $

Considering massless rigid rod and small oscillations, the natural frequency (in $rad/s$) of vibration of the system shown in the figure is$\sqrt{\dfrac{400}{1}} \\$$\sqr...

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GATE2017 ME-1: 21
In a metal forming operation when the material has just started yielding. the principal stresses are $\sigma_{1}=+180 MPa, \sigma_{2}=-100 MPa, \sigma_{3}=0$. Following von Mises' criterion, the yield stress is _________ MPa.

In a metal forming operation when the material has just started yielding. the principal stresses are $\sigma_{1}=+180 MPa, \sigma_{2}=-100 MPa, \sigma_{3}=0$. Following v...

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GATE2017 ME-2: 22
Given the atomic weight of Fe is $56$ and that of $C$ is $12$, the weight percentage of carbon in cementite $(Fe_{3}C)$ is _________.

Given the atomic weight of Fe is $56$ and that of $C$ is $12$, the weight percentage of carbon in cementite $(Fe_{3}C)$ is _________.

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GATE2017 ME-1: 20
Cylindrical pins of diameter $15^{\pm0.020}$ mm are being produced on a machine. Statistical quality control tests show a mean of $14.995$ mm and standard deviation of $0.004$ mm. The process capability index $Cp$ is $0.833$ $1.667$ $3.333$ $3.750$

Cylindrical pins of diameter $15^{\pm0.020}$ mm are being produced on a machine. Statistical quality control tests show a mean of $14.995$ mm and standard deviation of $0...

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GATE2017 ME-2: 7
The state of stress at a point is $\sigma _{x}=\sigma _{y}=\sigma _{z}=\tau _{xz}=\tau _{zx}=\tau _{yz}=\tau _{zy}=0$ and $\tau _{xy}=\tau _{yx}=50$ MPa. The maximum normal stress (in MPa) at that point is ________.

The state of stress at a point is $\sigma _{x}=\sigma _{y}=\sigma _{z}=\tau _{xz}=\tau _{zx}=\tau _{yz}=\tau _{zy}=0$ and $\tau _{xy}=\tau _{yx}=50$ MPa. The maximum norm...

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GATE2017 ME-2: 9
The cantilever beam of Length $L$ and Flexural modulus $EI$ is subjected to a point load $P$ at the free end. The elastic strain energy stored in the beam due to bending (neglecting transverse shear) is $\dfrac{P^{2}L^{3}}{6EI} \\$ $\dfrac{P^{2}L^{3}}{3EI} \\$ $\dfrac{PL^{3}}{3EI} \\$ $\dfrac{PL^{3}}{6EI}$

The cantilever beam of Length $L$ and Flexural modulus $EI$ is subjected to a point load $P$ at the free end. The elastic strain energy stored in the beam due to bending ...

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GATE2017 ME-1: 18
The damping ratio for a viscously damped spring-mass system, governed by the relationship $m \dfrac{d^{2}x}{dt^{2}}+c\dfrac{dx}{dt}+kx=F(t)$, is given by $\sqrt{\dfrac{c}{mk}} \\$ $\dfrac{c}{2\sqrt{km}} \\$ $\dfrac{c}{\sqrt{km}} \\$ $\sqrt{\dfrac{c}{2mk}}$

The damping ratio for a viscously damped spring-mass system, governed by the relationship $m \dfrac{d^{2}x}{dt^{2}}+c\dfrac{dx}{dt}+kx=F(t)$, is given by$\sqrt{\dfrac{c}{...

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GATE2015-2-36
A single-degree-freedom spring-mass system is subjected to a sinusoidal force of $10$ $N$ amplitude and frequency $ω$ along the axis of the spring. The stiffness of the spring is $150$ $N/m$, damping factor is $0.2$ and the undamped natural frequency is $10ω$. At steady state, the amplitude of vibration (in $m$) is approximately $0.05$ $0.07$ $0.70$ $0.90$

A single-degree-freedom spring-mass system is subjected to a sinusoidal force of $10$ $N$ amplitude and frequency $ω$ along the axis of the spring. The stiffness of the ...

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GATE2017 ME-2: 23
For a single server with Poisson and exponential service time, the arrival rate is $12$ per hour. Which one of the following service rates will provide a steady state finite queue length? $6$ per hour $10$ per hour $12$ per hour $24$ per hour

For a single server with Poisson and exponential service time, the arrival rate is $12$ per hour. Which one of the following service rates will provide a steady state fin...

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GATE2016-3-32
A rigid rod $(AB)$ of length $L=\sqrt{2} \: m$ is undergoing translational as well as rotational motion in the $x-y$ plane (see the figure). The point $A$ has the velocity $V_1=\hat{i}+2\hat{j} \: m/s$. The end B is constrained to move only along the $x$ direction. The magnitude of the velocity $V_2$ (in $m/s$) at the end B is __________

A rigid rod $(AB)$ of length $L=\sqrt{2} \: m$ is undergoing translational as well as rotational motion in the $x-y$ plane (see the figure). The point $A$ has the velocit...

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GATE2017 ME-2: 6
A mass $m$ is attached to two identical springs having spring constant $k$ as shown in the figure. The natural frequency $\omega$ of this single degree of freedom system is $\sqrt{\dfrac{2k}{m}} \\$ $\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{k}{2m}} \\ $ $\sqrt{\dfrac{4k}{m}}$

A mass $m$ is attached to two identical springs having spring constant $k$ as shown in the figure. The natural frequency $\omega$ of this single degree of freedom system ...

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