Recent questions tagged applied-mechanics-and-design / GO Mechanical

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GATE2018-1-19
A steel column of rectangular section ($15$ mm $\times \: 10$ mm) and length $1.5$ m is simply supported at both ends. Assuming modulus of elasticity, $E=200$ GPa for steel, the critical axial load (in kN) is ______ (correct to two decimal places).

A steel column of rectangular section ($15$ mm $\times \: 10$ mm) and length $1.5$ m is simply supported at both ends. Assuming modulus of elasticity, $E=200$ GPa for ste...

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GATE2018-1-11
In a linearly hardening plastic material, the true stress beyond initial yielding increases linearly with the true strain decreases linearly with the true strain first increases linearly and then decreases linearly with the true strain remains constant

In a linearly hardening plastic material, the true stress beyond initial yieldingincreases linearly with the true straindecreases linearly with the true strainfirst incre...

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GATE2018-1-8
For an Oldham coupling used between two shafts, which among the following statements are correct? Torsional load is transferred along shaft axis A velocity ratio of $1:2$ between shafts is obtained without using gears Bending load id transferred transverse to shaft axis Rotation is transferred along shaft axis I and III I and IV II and III II and IV

For an Oldham coupling used between two shafts, which among the following statements are correct?Torsional load is transferred along shaft axisA velocity ratio of $1:2$ b...

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GATE2018-1-7
The equation of motion for a spring-mass system excited by a harmonic force is $M\ddot{x} + K x = F \cos(\omega t)$, where $M$ is the mass, $K$ is the spring stiffness, $F$ is the force amplitude and $\omega$ is the angular frequency of excitation. Resonance occurs when $\omega$ is equal ... $2 \pi \sqrt{\dfrac{K}{M}} \\$ $\sqrt{\dfrac{K}{M}}$

The equation of motion for a spring-mass system excited by a harmonic force is $M\ddot{x} + K x = F \cos(\omega t)$, where $M$ is the mass, $K$ is the spring stiffness, $...

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GATE2018-1-6
If $\sigma_1$ and $\sigma_3$ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is $\dfrac{\sigma_1 +\sigma_3}{2} \\$ $\dfrac{\sigma_1 -\sigma_3}{2} \\ $ $\sqrt{\dfrac{\sigma_1 +\sigma_3}{2}} \\$ $\sqrt{\dfrac{\sigma_1 -\sigma_3}{2}}$

If $\sigma_1$ and $\sigma_3$ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is$\dfrac{\sigma_1 +\sigma_...

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GATE2018-1-5
A bar of uniform cross section and weighing $100 \:N$ is held horizontally using two massless and inextensible strings $S1$ and $S2$ as shown in the figure The tensions in the strings are $T_1=100 \: N \text{ and } T_2=0 \: N$ $T_1=0 \: N \text{ and } T_2=100 \: N$ $T_1=75 \: N \text{ and } T_2=25 \: N$ $T_1=25 \: N \text{ and } T_2=75 \: N$

A bar of uniform cross section and weighing $100 \:N$ is held horizontally using two massless and inextensible strings $S1$ and $S2$ as shown in the figureThe tensions in...

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GATE2017 ME-2: 50
A rod of length $20$ mm is stretched to make a rod of length $40$ mm. Subsequently, it is compressed to make a rod of final length $10$ mm. Consider the longitudinal tensile strain as positive and compressive strain as negative. The total true longitudinal strain in the rod is $-0.5$ $-0.69$ $-0.75$ $-1.0$

A rod of length $20$ mm is stretched to make a rod of length $40$ mm. Subsequently, it is compressed to make a rod of final length $10$ mm. Consider the longitudinal tens...

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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: 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-2: 36
A single-plate clutch has a friction disc with inner and outer radii of $20$ mm and $40$ mm, respectively. The friction lining in the disc is made in such a way that the coefficient of friction $\mu$ varies radially as $\mu=0.01r$, where $r$ is in ... to transmit a friction torque of $18.85$ kN.mm. As per uniform pressure theory, the pressure (in MPa) on the disc is ________.

A single-plate clutch has a friction disc with inner and outer radii of $20$ mm and $40$ mm, respectively. The friction lining in the disc is made in such a way that the ...

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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-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: 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: 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-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-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: 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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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-2: 21
The crystal structure of aluminium is. body-centered cubic. face-centered cubic. close-packed hexagonal. body-centered tetragonal.

The crystal structure of aluminium is.body-centered cubic.face-centered cubic.close-packed hexagonal.body-centered tetragonal.

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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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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-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-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: 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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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: 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-1: 46
A thin uniform rigid bar of Length $L$ and mass $M$ is hinged at point $O$, located at a distance of $\dfrac{L}{3}$ from one of its ends. The bar is further supported using springs, each of stiffness $k$, located at the two ends. A particle of mass $m=\dfrac{M}{4}$ is fixed at ... $\sqrt{\dfrac{5k}{2M}} \\$ $\sqrt{\dfrac{3k}{2M}} \\$ $\sqrt{\dfrac{3k}{M}}$

A thin uniform rigid bar of Length $L$ and mass $M$ is hinged at point $O$, located at a distance of $\dfrac{L}{3}$ from one of its ends. The bar is further supported usi...

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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-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-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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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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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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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: 25
In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers to Yield stress Proportional limit Maximum stress Fracture stress

In the engineering stress-strain curve for mild steel, the Ultimate Tensile Strength (UTS) refers toYield stressProportional limitMaximum stressFracture stress

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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-1: 19
Consider the schematic of a riveted lap joint subjected to tensile load $F$, as shown below. Let $d$ be the diameter of the rivets, and $S_{f}$ be the maximum permissible tensile stress in the plates. What should be the minimum value for the thickness of the plates to guard against tensile failure of ... $\dfrac{F}{S_{f}W} \\$ $\dfrac{F}{S_{f}(W-d)} \\$ $\dfrac{2F}{S_{f}W}$

Consider the schematic of a riveted lap joint subjected to tensile load $F$, as shown below. Let $d$ be the diameter of the rivets, and $S_{f}$ be the maximum permissible...

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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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GATE2017 ME-1: 17
The following figure shows the velocity-time plot for a particle travelling along a straight line. The distance covered by the particle from $t=0$ to $t=5$s is __________ m.

The following figure shows the velocity-time plot for a particle travelling along a straight line. The distance covered by the particle from $t=0$ to $t=5$s is __________...

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GATE2017 ME-1: 16
Consider a beam with circular cross-section of diameter $d$. The ratio of the second moment of area about the neutral axis to the section modulus of the area is $\dfrac{d}{2} \\$ $\dfrac{\pi d}{2} \\$ $d \\$ $\pi d$

Consider a beam with circular cross-section of diameter $d$. The ratio of the second moment of area about the neutral axis to the section modulus of the area is$\dfrac{d}...

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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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