Most viewed questions in Applied Mechanics and Design / GO Mechanical

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GATE2016-2-32
A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends as shown in the figure. The shear modulus for the cylinder is $G$ and the Young’s modulus is $E$. The vertical deflection at point A is $PL^3/(\pi R^4G)$ $PL^3/(\pi R^4E)$ $2PL^3/(\pi R^4E)$ $4PL^3/(\pi R^4G)$

A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends a...

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GATE Mechanical 2014 Set 3 | Question: 18
The process utilizing mainly thermal energy for removing material is Ultrasonic Matching Electrochemical Matching Abrasive Jet Matching Laser Beam Matching

The process utilizing mainly thermal energy for removing material isUltrasonic MatchingElectrochemical Matching Abrasive Jet MatchingLaser Beam Matching

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GATE2020-ME-1: 21
A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of $10\:\text{grams}$, attached to four points on the $100\: mm$ radius circle shown in the figure. The rotor is driven bt a motor at uniform angular speed of ... gets detached then the magnitude of the resultant unbalance force on the rotor is ________$N$ (rounded off to $2$ decimal places).

A balanced rigid disc mounted on a rigid rotor has four identical point masses, each of $10\:\text{grams}$, attached to four points on the $100\: mm$ radius circle shown ...

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GATE2020-ME-1: 39
A rectangular steel bar of length $500\: mm$, width $100\: mm$, and thickness $15\: mm$ is cantilevered to a $200\: mm$ steel channel using $4$ bolts, as shown For an external load of $10\: kN$ applied at the tip of the steel bar, the resultant shear load on the bolt at $B$, is _______$kN$ (round off to one decimal place).

A rectangular steel bar of length $500\: mm$, width $100\: mm$, and thickness $15\: mm$ is cantilevered to a $200\: mm$ steel channel using $4$ bolts, as shownFor an exte...

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GATE ME 2012 | Question: 2
Match the following metal forming process with their associated stresses in the workpiece. ... $1-S; 2-P; 3-R; 4-Q$ $1-P; 2-Q; 3-S; 4-R$ $1-P; 2-R; 3-Q; 4-S$

Match the following metal forming process with their associated stresses in the workpiece.$\begin{array}{llll} {} & \textbf{Metal forming process} & {} & \textbf{Type of ...

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GATE2018-1-30
An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are $20$, $30$ and $20$, respectively. Gear C has $80$ teeth on the inner surface and $100$ teeth on the outer surface. If the carrier arm AB is fixed and the ... A rotates at $300$ rpm in the clockwise direction, then the rpm of D in the clockwise direction is $240$ $-240$ $375$ $-375$

An epicyclic gear train is shown in the figure below. The number of teeth on the gears A, B and D are $20$, $30$ and $20$, respectively. Gear C has $80$ teeth on the inne...

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GATE2015-3-48
A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________

A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________

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GATE Mechanical 2014 Set 1 | Question: 8
Critical damping is the largest amount of damping for which no oscillation occurs in free vibration smallest amount of damping for wh ich no oscillation occurs in free vibration largest amount of damping for which the motion is simple harmonic in f ree vibration smallest amount of dam ping for which the motion is simple harmonic in free vibration

Critical damping is thelargest amount of damping for which no oscillation occurs in free vibrationsmallest amount of damping for wh ich no oscillation occurs in free vibr...

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GATE ME 2013 | Question: 41
A simply supported beam of length $L$ is subjected to a varying distributed load $\sin(3\pi x/L) Nm^{-1}$ , where the distance $x$ is measured from the left support. The magnitude of the vertical reaction force in $N$ at the left support is $\text{zero}$ $L/3\pi$ $L/\pi$ $2L/\pi$

A simply supported beam of length $L$ is subjected to a varying distributed load $\sin(3\pi x/L) Nm^{-1}$ , where the distance $x$ is measured from the left support. The ...

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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: 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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GATE2019 ME-1: 42
At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all other stress components are zero. The yield strength of the material is $468 \: MPa$ The factor of safety on the basis of maximum shear stress theory is ___________ (round off to one decimal place)

At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all o...

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GATE2018-2-30
A rigid rod of length $1 \: m$ is resting at an angle $\theta =45^{\circ}$ as shown in the figure. The end $P$ is dragged with a velocity of $U=5 \: m/s$ to the right. At the instant shown, the magnitude of the velocity $V$ (in $m/s$) of point $Q$ as it moves along the wall without losing contact is $5$ $6$ $8$ $10$

A rigid rod of length $1 \: m$ is resting at an angle $\theta =45^{\circ}$ as shown in the figure. The end $P$ is dragged with a velocity of $U=5 \: m/s$ to the right. At...

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GATE2016-1-33
The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in $mm^4$) of this cross-section about its base is ________

The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in $mm^4$) of this cross-section about its base is ________

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GATE2019 ME-1: 43
A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk center $A$ ... disk. For small disturbance from the equilibrium, the natural frequency of vibration of the system is _________ $rad/s$ (round off to oe decimal place).

A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk c...

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GATE2018-1-54
Block $P$ of mass $2$ kg slides down the surface and has a speed $20 \: m/s$ at the lowest point, $Q$, where the local radius of curvature is $2$ m as shown in the figure. Assuming $g=10 \: m/s^2$, the normal force (in $N$) at $Q$ is ____ correct to two decimal places.

Block $P$ of mass $2$ kg slides down the surface and has a speed $20 \: m/s$ at the lowest point, $Q$, where the local radius of curvature is $2$ m as shown in the figure...

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GATE2016-2-30
A mass of $2000$ $kg$ is currently being lowered at a velocity of $2$ $m/s$ from the drum as shown in the figure. The mass moment of inertia of the drum is $150$ $kg$-$m^2$. On applying the brake, the mass is brought to rest in a distance of $0.5$ $m$. The energy absorbed by the brake (in $kJ$) is __________

A mass of $2000$ $kg$ is currently being lowered at a velocity of $2$ $m/s$ from the drum as shown in the figure. The mass moment of inertia of the drum is $150$ $kg$-$m^...

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GATE2015-2-11
The uniaxial yield stress of a material is $300$ $MPa$. According to von Mises criterion, the shear yield stress (in $MPa$) of the material is _______

The uniaxial yield stress of a material is $300$ $MPa$. According to von Mises criterion, the shear yield stress (in $MPa$) of the material is _______

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GATE Mechanical 2014 Set 3 | Question: 53
The diameter of a recessed ring was measured by using two spherical balls of diameter $d_2$ = $60$ $mm$ and $d_1$ = $40$ $mm$ as shown in the figure. The distance $H_2$ = $35.55$ $mm$ and $H_1$ = $20.55$ $mm$. The diameter ($D$, in $mm$) of the ring gauge is _______

The diameter of a recessed ring was measured by using two spherical balls of diameter $d_2$ = $60$ $mm$ and $d_1$ = $40$ $mm$ as shown in the figure.The distance $H_2$ = ...

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GATE Mechanical 2014 Set 3 | Question: 35
A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to zero? $0.5L$ $0.25L$ $0.33L$ $0.66L$

A force $P$ is applied at a distance $x$ from the end of the beam as shown in the figure. What would be the value of $x$ so that the displacement at ‘$A$’ is equal to...

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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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GATE2015-1-41
A pinion with radius $r_1$, and inertia $I_1$ is driving a gear with radius $r_2$ and inertia $I_2$. Torque $\tau _1$ is applied on pinion. The following are free body diagrams of pinion and gear showing important forces ($F_1$ and $F_2$) of interaction. Which of the following ... $F_2=I_2\dfrac{1}{r_2}\ddot{\theta _1};$

A pinion with radius $r_1$, and inertia $I_1$ is driving a gear with radius $r_2$ and inertia $I_2$. Torque $\tau _1$ is applied on pinion. The following are free body di...

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GATE Mechanical 2014 Set 3 | Question: 55
For spot welding of two steel sheets (base metal) each of $3$ $mm$ thickness, welding current of $10000$ $A$ is applied for $0.2$ $s$. The heat dissipated to the base metal is $1000$ $J$ ... $J$ and interfacial contact resistance between sheets is $0.0002$ $Ω$, the volume (in $mm^3$) of weld nugget is _______

For spot welding of two steel sheets (base metal) each of $3$ $mm$ thickness, welding current of $10000$ $A$ is applied for $0.2$ $s$. The heat dissipated to the base met...

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GATE Mechanical 2014 Set 3 | Question: 40
A mass-spring-dashpot system with mass $m = 10$ $kg$, spring constant $k = 6250$ $N/m$ is excited by a harmonic excitation of $10 cos(25t)$ $N$. At the steady state, the vibration amplitude of the mass is $40$ $mm$. The damping coefficient ($c$, in $N.s/m$) of the dashpot is _______

A mass-spring-dashpot system with mass $m = 10$ $kg$, spring constant $k = 6250$ $N/m$ is excited by a harmonic excitation of $10 cos(25t)$ $N$. At the steady state, the ...

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GATE ME 2012 | Question: 21
A circular solid disc of uniform thickness of $20$ mm, radius $200$ mm and mass $20$ kg, is used as a flywheel. If it rotates at $600$ rpm, the kinetic energy of the flywheel, in $\textit{Joules}$ is $395$ $790$ $1580$ $3160$

A circular solid disc of uniform thickness of $20$ mm, radius $200$ mm and mass $20$ kg, is used as a flywheel. If it rotates at $600$ rpm, the kinetic energy of the flyw...

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GATE ME 2013 | Question: 21
A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal stress developed in the shell is $0.5$ $1.0$ $2.0$ $4.0$

A long thin walled cylindrical shell, closed at both the ends, is subjected to an internal pressure. The ratio of the hoop stress (circumferential stress) to longitudinal...

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GATE2019 ME-1: 44
A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coefficient of friction is $0.25$. The value of $a$ in mm (round off to one decimal place), such that the minimum actuating force $P$ is $2000 \: N$, is ___________

A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coeffi...

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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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GATE2016-2-36
The rod $AB$, of length $1$ $m$, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along $QP$ and $QR$. If the velocity $VA$ of the slider at $A$ is $2$ $m/s$, the velocity of the midpoint of the rod at this instant is ___________ $m/s$.

The rod $AB$, of length $1$ $m$, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along $QP$ and $QR$. If the velocity $VA$...

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GATE2015-3-27
Figure shows a wheel rotating about $O_2$. Two points $A$ and $B$ located along the radius of wheel have speeds of $80$ $m/s$ and $140$ $m/s$ respectively. The distance between the points $A$ and $B$ is $300$ $mm$. The diameter of the wheel (in $mm$) is ________

Figure shows a wheel rotating about $O_2$. Two points $A$ and $B$ located along the radius of wheel have speeds of $80$ $m/s$ and $140$ $m/s$ respectively. The distance b...

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GATE ME 2013 | Question: 7
For steady, fully developed flow inside a straight pipe of diameter $D$, neglecting gravity effects, the pressure drop $\Delta p$ over a length $L$ and the wall shear stress $\tau _\omega$ are related by $\tau _\omega =\dfrac{\Delta pD}{4L} \\$ $\tau _\omega =\dfrac{\Delta pD^2}{4L^2} \\$ $\tau _\omega =\dfrac{\Delta pD}{2L} \\$ $\tau _\omega =\dfrac{4\Delta p L}{D}$

For steady, fully developed flow inside a straight pipe of diameter $D$, neglecting gravity effects, the pressure drop $\Delta p$ over a length $L$ and the wall shear st...

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GATE2015-2-33
A cantilever beam with square cross-section of $6 \: mm$ side is subjected to a load of $2 \: kN$ normal to the top surface as shown in the figure. The Young’s modulus of elasticity of the material of the beam is $210 \: GPa$. The magnitude of slope (in radian) at $Q$ ($20 \: mm$ from the fixed end) is ________

A cantilever beam with square cross-section of $6 \: mm$ side is subjected to a load of $2 \: kN$ normal to the top surface as shown in the figure. The Young’s modulus ...

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GATE ME 2013 | Question: 48
A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details. width of the plate w = $200$ $mm$, thickness of the plate $t$ = $5$ $mm$, number of rivets $n$ = $3$, diameter of the rivet ... be designed to avoid crushing failure, the maximum permissible load $P$ in $kN$ is $7.50$ $15.00$ $22.50$ $30.00$

A single riveted lap joint of two similar plates as shown in the figure below has the following geometrical and material details.width of the plate w = $200$ $mm$, thickn...

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GATE Mechanical 2014 Set 2 | Question: 32
For the three bolt system shown in the figure, the bolt material has shear yield strength of $200$ $MPa$. For a factor of safety of $2$, the minimum metric specification required for the bolt is $M8$ $M10$ $M12$ $M16$

For the three bolt system shown in the figure, the bolt material has shear yield strength of $200$ $MPa$. For a factor of safety of $2$, the minimum metric specification ...

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GATE Mechanical 2014 Set 2 | Question: 37
Maximum fluctuation of kinetic energy in an engine has been calculated to be $2600$ $J$. Assuming that the engine runs at an average speed of $200$ $rpm$, the polar mass moment of inertia (in $kg.m^2$) of a flywheel to keep the speed fluctuation within $±0.5$% of the average speed is _______

Maximum fluctuation of kinetic energy in an engine has been calculated to be $2600$ $J$. Assuming that the engine runs at an average speed of $200$ $rpm$, the polar mass ...

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GATE ME 2013 | Question: 5
Two threaded bolts $A$ and $B$ of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt $A$ is $4$ times that of bolt $B$ and the mean diameter of bolt $A$ is $12$ $mm$, the mean diameter of bolt $B$ in $mm$ is $16$ $24$ $36$ $48$

Two threaded bolts $A$ and $B$ of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt $A$ is $4$ times that of b...

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GATE2016-3-12
Which of the bearings given below SHOULD NOT be subjected to a thrust load? Deep groove ball bearing Angular contact ball bearing Cylindrical (straight) roller bearing Single row tapered roller bearing

Which of the bearings given below SHOULD NOT be subjected to a thrust load?Deep groove ball bearingAngular contact ball bearingCylindrical (straight) roller bearingSingle...

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GATE2016-2-34
In the figure, the load $P=1 \: N$, length $L=1 \: m$, Young’s modulus $E=70 \: GPa$, and the cross-section of the links is a square with dimension $10 \: mm \times 10 \: mm$. All joints are pin joints. The stress (in $Pa$) in the link $AB$ is ___________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

In the figure, the load $P=1 \: N$, length $L=1 \: m$, Young’s modulus $E=70 \: GPa$, and the cross-section of the links is a square with dimension $10 \: mm \times 10 ...

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GATE2015-2-30
The initial velocity of an object is $40$ $m/s$. The acceleration a of the object is given by the following expression: $a=-0.1v$ where $v$ is the instantaneous velocity of the object. The velocity of the object after $3$ seconds will be _______

The initial velocity of an object is $40$ $m/s$. The acceleration a of the object is given by the following expression: ...

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GATE Mechanical 2014 Set 2 | Question: 30
The flexural rigidity $(EI)$ of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ ... $\dfrac{PL^2}{EI} \\$ $\dfrac{3}{2}\dfrac{PL^2}{EI} \\$ $\dfrac{5}{2}\dfrac{PL^2}{EI}$

The flexural rigidity $(EI)$ of a cantilever beam is assumed to be constant over the length of the beam shown in figure. If a load $P$ and bending moment $PL/2$ are appli...

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