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GATE2019 ME-1: 6
The natural frequencies corresponding to the spring-mass systems $I$ and $II$ are $\omega_1$ and $\omega_{II}$, respectively. The ratio $\dfrac{\omega_I}{\omega_{II}}$ is $\dfrac{1}{4} \\$ $\dfrac{1}{2} \\$ $2 \\$ $4$

The natural frequencies corresponding to the spring-mass systems $I$ and $II$ are $\omega_1$ and $\omega_{II}$, respectively. The ratio $\dfrac{\omega_I}{\omega_{II}}$ is...

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GATE2018-1-28
A point mass is shot vertically up from ground level with a velocity of $4$ m/s at time, $t=0$. It loses $20 \%$ of its impact velocity after each collision with the ground. Assuming that the acceleration due to gravity is $10 \: m/s^2$ and that air resistance ... , the mass stops bouncing and comes to complete rest on the ground after a total time (in seconds) of $1$ $2$ $4$ $\infty$

A point mass is shot vertically up from ground level with a velocity of $4$ m/s at time, $t=0$. It loses $20 \%$ of its impact velocity after each collision with the grou...

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GATE2016-3-34
Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\theta _S$ is the twist and $\tau _S$ ... $\theta _S<\theta _H$ and $\tau _S<\tau _H$ $\theta _S=\theta _H$ and $\tau _S<\tau _H$

Two circular shafts made of same material, one solid (S) and one hollow (H), have the same length and polar moment of inertia. Both are subjected to same torque. Here, $\...

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GATE2019 ME-1: 30
In a four bar planar mechanism shown in the figure, $AB= 5 \: cm, AD=4 \: cm $ and $DC=2 \: cm$. In the configuration shown, both AB and DC are perpendicular to AD. The bar AB rotates with an angular velocity of $10 \: rad/s$. The magnitude of angular velocity (in rad/s) of bar DC at this instant is $0$ $10$ $15$ $25$

In a four bar planar mechanism shown in the figure, $AB= 5 \: cm, AD=4 \: cm $ and $DC=2 \: cm$. In the configuration shown, both AB and DC are perpendicular to AD. The b...

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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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GATE Mechanical 2014 Set 4 | Question: 34
A uniform slender rod ($8$ $m$ length and $3$ $kg$ mass) rotates in a vertical plane about a horizontal axis $1$ $m$ from its end as shown in the figure. The magnitude of the angular acceleration (in $rad/s^2$) of the rod at the position shown is _______

A uniform slender rod ($8$ $m$ length and $3$ $kg$ mass) rotates in a vertical plane about a horizontal axis $1$ $m$ from its end as shown in the figure. The magnitude of...

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GATE2020-ME-2: 10
Two plates, each of $6$ mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affected zone. Arc welding MIG welding Laser beam welding Submerged arc welding $1-4-2-3$ $3-4-2-1$ $4-3-2-1$ $3-2-4-1$

Two plates, each of $6$ mm thickness, are to be butt-welded. Consider the following processes and select the correct sequence in increasing order of size of the heat affe...

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GATE2019 ME-1: 7
A spur gear with $20^{\circ}$ full depth teeth is transmitting $20 \: kW$ at $200 \: rad/s$. The pitch circle diameter of the gear is $100 \: mm$. The magnitude of the force applied on the gear in the radial direction is $0.36 \: kN$ $0.73 \: kN$ $1.39 \: kN$ $2.78 \: kN$

A spur gear with $20^{\circ}$ full depth teeth is transmitting $20 \: kW$ at $200 \: rad/s$. The pitch circle diameter of the gear is $100 \: mm$. The magnitude of the fo...

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GATE Mechanical 2014 Set 2 | Question: 11
A thin plate of uniform thickness is subject to pressure as shown in the figure below Under the assumption of plane stress, which one of the following is correct? Normal stress is zero in the z-direction Normal stress is tensile in the z-direction Normal stress is compressive in the z-direction Normal stress varies in the z-direction

A thin plate of uniform thickness is subject to pressure as shown in the figure belowUnder the assumption of plane stress, which one of the following is correct?Normal st...

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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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GATE Mechanical 2014 Set 3 | Question: 51
A manufacturer can produce $12000$ bearings per day. The manufacturer received an order of $8000$ bearings per day from a customer. The cost of holding a bearing in stock is $Rs$. $0.20$ per month. Setup cost per production run is $Rs$. $50 0$. Assuming ... in a year, the frequency of production run should be $4.5$ days $4.5$ months $6.8$ days $6.8$ months

A manufacturer can produce $12000$ bearings per day. The manufacturer received an order of $8000$ bearings per day from a customer. The cost of holding a bearing in stock...

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GATE Mechanical 2014 Set 2 | Question: 34
What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denoted by m and the spring constants are denoted by $k_1$ and $k_2$ ... $\sqrt{\dfrac{k_1-k_2}{m}} \\$ $\sqrt{\dfrac{k_1+k_2}{m}}$

What is the natural frequency of the spring mass system shown below? The contact between the block and the inclined plane is frictionless. The mass of the block is denote...

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GATE Mechanical 2014 Set 2 | Question: 35
A disc clutch with a single friction surface has coefficient of friction equal to $0.3$. The maximum pressure which can be imposed on the friction material is $1.5$ $MPa$. The outer diameter of the clutch plate is $200$ $mm$ and its ... $mm$. Assuming uniform wear theory for the clutch plate, the maximum torque (in $N.m$) that can be transmitted is _______

A disc clutch with a single friction surface has coefficient of friction equal to $0.3$. The maximum pressure which can be imposed on the friction material is $1.5$ $MPa$...

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GATE2015-1-46
A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude of the load on the worst loaded rivet (in $N$) is _______

A horizontal plate has been joined to a vertical post using four rivets arranged as shown in the figure. The magnitude of the load on the worst loaded rivet (in $N$) is _...

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GATE ME 2012 | Question: 43
A solid circular shaft needs to be designed to transmit a torque of $50$ N.m. If the allowable shear stress of the material is $140$ MPa, assuming a factor of safety of $2$, the minimum allowable design diameter in mm is $8$ $16$ $24$ $32$

A solid circular shaft needs to be designed to transmit a torque of $50$ N.m. If the allowable shear stress of the material is $140$ MPa, assuming a factor of safety of $...

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GATE ME 2012 | Question: 9
A solid disc of radius $r$ rolls without slipping on a horizontal floor with angular velocity $\omega$ and angular acceleration $\alpha$. The magnitude of the acceleration of the point of contract on the disc is $zero$ $r \alpha$ $\sqrt{(r \alpha)^2 + (r \omega^2)^2}$ $r \omega^2$

A solid disc of radius $r$ rolls without slipping on a horizontal floor with angular velocity $\omega$ and angular acceleration $\alpha$. The magnitude of the acceleratio...

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GATE2016-1-34
A simply-supported beam of length $3L$ is subjected to the loading shown in the figure. It is given that $P=1\: N$, $L=1\:m$ and Young's modulus $E=200\:GPa$. The cross-section is a square with dimension $10\:mm\times10\:mm$. The ... at a distance of $1.5L$ from the left end is _____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

A simply-supported beam of length $3L$ is subjected to the loading shown in the figure.It is given that $P=1\: N$, $L=1\:m$ and Young’s modulus $E=200\:GPa$. The cross-...

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GATE2020-ME-1: 6
A single-degree-of-freedom oscillator is subjected to harmonic excitation $F(t) = F_{0}\cos(\omega t)$ as shown in the figure. The non-zero value of $\omega$, for which the amplitude of the force transmitted to the ground will be $F_{0}$, is $\sqrt{\dfrac{k}{2m}} \\$ $\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{2k}{m}} \\$ $2\sqrt{\dfrac{k}{m}}$

A single-degree-of-freedom oscillator is subjected to harmonic excitation $F(t) = F_{0}\cos(\omega t)$ as shown in the figure. The non-zero value of $\omega$,...

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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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GATE2016-1-51
A cylindrical job with diameter of $200$ $mm$ and height of $100$ $mm$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical riser does not contribute as cooling surface. If the diameter of the riser is equal to its height, then the height of the riser (in $mm$) is $150$ $200$ $100$ $125$

A cylindrical job with diameter of $200$ $mm$ and height of $100$ $mm$ is to be cast using modulus method of riser design. Assume that the bottom surface of cylindrical r...

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GATE2018-1-48
The true stress $(\sigma)$ - true strain $(\varepsilon)$ diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to stress of $500$ MPa and strain of $0.5$. Then from point A, there is ... . Given that the Young's modulus $E=200$ GPa, te natural strain at point B$(\varepsilon_B)$ is _____ (correct to three decimal places)

The true stress $(\sigma)$ - true strain $(\varepsilon)$ diagram of a strain hardening material is shown in figure. First, there is loading up to point A, i.e., up to str...

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GATE2016-3-38
A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200N-m$ is acting on the joint. Neglecting friction due to clamping force, maximum shear stress in a bolt is ______ $MPa$.

A bolted joint has four bolts arranged as shown in figure. The cross sectional area of each bolt is $25$ $mm^2$. A torque $T$ = $200N-m$ is acting on the joint. Neglectin...

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GATE2018-2-32
In a cam-follower, the follower rises by $h$ as the cam rotates by $\delta$ (radians) at constant angular velocity $\omega$ (radians/s). The follower is uniformly accelerating during the first half of the rise period and it is uniformly decelerating in the latter half of the rise period ... is $\dfrac{4h \omega}{\delta} \\$ $h \omega \\$ $\dfrac{2h \omega}{\delta} \\$ $2h \omega$

In a cam-follower, the follower rises by $h$ as the cam rotates by $\delta$ (radians) at constant angular velocity $\omega$ (radians/s). The follower is uniformly acceler...

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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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GATE2019 ME-1: 34
A plane-strain compression (forging) of a block is shown in the figure. The strain in the $z$-direction is zero. The yield strength $(S_y)$ in uniaxial tension/compression of the material of the block is $300 \: MPa$ and it follows the Tresca (maximum shear stress) ... $340 \: MPa$ (compressive) $340 \: MPa$ (tensile) $260 \: MPa$ (compressive) $260 \: MPa$ (tensile)

A plane-strain compression (forging) of a block is shown in the figure. The strain in the $z$-direction is zero. The yield strength $(S_y)$ in uniaxial tension/compressio...

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GATE2018-2-39
A force of $100 \: N$ applied to the centre of a circular disc, of mass $10 \: kg$ and radius $1 \: m$, resting on a floor as shown in the figure. If the disc rolls without slipping on the floor, the linear acceleration (in $m/s^2$) of the centre of the disc is _______ (correct to two decimal places).

A force of $100 \: N$ applied to the centre of a circular disc, of mass $10 \: kg$ and radius $1 \: m$, resting on a floor as shown in the figure. If the disc rolls witho...

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GATE2015-3-2
For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation OO’ passing through the center of gravity.

For the same material and the mass, which of the following configurations of flywheel will have maximum mass moment of inertia about the axis of rotation OO’ passing th...

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GATE2015-1-37
In a slab rolling operation, the maximum thickness reduction $(Δℎ_{max}$) is given by $Δ_{max}$ = $\mu^2R$ , where $R$ is the radius of the roll and $\mu$ is the coefficient of friction between the roll and the sheet. If $\mu$ = $0.1$, the maximum angle subtended by the deformation zone at the centre of the roll (bite angle in degrees) is _______

In a slab rolling operation, the maximum thickness reduction $(Δℎ_{max}$) is given by $Δ_{max}$ = $\mu^2R$ , where $R$ is the radius of the roll and $\mu$ is the coef...

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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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GATE2015-3-3
A gear train is made up of five spur gears as shown in the figure. Gear $2$ is driver and gear $6$ is driven member. $N_2$, $N_3$, $N_4$, $N_5$ and $N_6$ represent number of teeth on gears $2$, $3$, $4$, $5$, and $6$ respectively. The gear(s) which act(s) as idler(s) is/are Only $3$ Only $4$ Only $5$ Both $3$ and $5$

A gear train is made up of five spur gears as shown in the figure. Gear $2$ is driver and gear $6$ is driven member. $N_2$, $N_3$, $N_4$, $N_5$ and $N_6$ represent number...

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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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GATE Mechanical 2014 Set 2 | Question: 7
A two member truss ABC is shown in the figure. The force (in $kN$) transmitted in member AB is _______

A two member truss ABC is shown in the figure. The force (in $kN$) transmitted in member AB is _______

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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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GATE2016-1-32
A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respectively. For the deflection at $C$ to be zero, the ratio $\displaystyle{\frac{P}{F}}$ is ____________

A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respe...

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GATE ME 2012 | Question: 34
The state of stress at a point under plane stress condition is $\sigma_{xx} = 40 \: MPa, \: \: \sigma_{yy} = 100 \: MPa \: \: \text{and }\tau_{xy} =40 \: Mpa$ The radius of the Mohr's circle representing the given state of stress in $MPa$ is $40$ $50$ $60$ $100$

The state of stress at a point under plane stress condition is $$\sigma_{xx} = 40 \: MPa, \: \: \sigma_{yy} = 100 \: MPa \: \: \text{and }\tau_{xy} =40 \: Mpa$$ The radiu...

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GATE ME 2012 | Question: 22
A cantilever beam of length $L$ is subjected to a moment $M$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $I$ and the Young's modulus is $E$. The magnitude of the maximum deflection is $\dfrac{ML^2}{2EI} \\$ $\dfrac{ML^2}{EI} \\$ $\dfrac{2ML^2}{EI} \\$ $\dfrac{4ML^2}{EI}$

A cantilever beam of length $L$ is subjected to a moment $M$ at the free end. The moment of inertia of the beam cross section about the neutral axis is $I$ and the Young'...

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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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GATE Mechanical 2014 Set 4 | Question: 40
A ladder AB of length $5$ $m$ and weight $(W)$ $600$ $N$ is resting against a wall. Assuming frictionless contact at the floor $(B)$ and the wall $(A)$, the magnitude of the force $P$ (in newton) required to maintain equilibrium of the ladder is _______

A ladder AB of length $5$ $m$ and weight $(W)$ $600$ $N$ is resting against a wall. Assuming frictionless contact at the floor $(B)$ and the wall $(A)$, the magnitude of ...

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GATE Mechanical 2014 Set 1 | Question: 52
During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produced is $0.5$ $mm$. The feed given to the zero degree rake angle tool is $0.2$ $mm/rev$. The shear strain produced during the operation is _______

During pure orthogonal turning operation of a hollow cylindrical pipe, it is found that the thickness of the chip produced is $0.5$ $mm$. The feed given to the zero degre...

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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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