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

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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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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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GATE2019 ME-1: 19
A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the block is $0.2$. A horizontal force of $10$ N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is _____

A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the bloc...

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GATE2019 ME-1: 20
A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear strain in the rod is $p \times 10^{-3}$, then $p$ is equal to ____ (round off to two decimal places).

A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear ...

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GATE2019 ME-1: 22
During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (minimum stress to maximum stress) for this cyclic loading is _____ (round off to one decimal place)

During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (m...

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GATE2019 ME-1: 25
Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. Upon loading, the stress-strain curve passes through initial yield point at $P$, and then ... specimen is reloaded in tension from point $R$, the value of stress at which the material yields again is _______ MPa.

Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. U...

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GATE2019 ME-1: 29
A car having weight $W$ is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height $h$ from the ground, midway between the front and rear wheels. The distance between front and rear wheel is $l$. The acceleration of the car is $a$, and ... $R_f=R_r = \dfrac{W}{2}+\dfrac{W}{g} \bigg( \dfrac{h}{l} \bigg) a$

A car having weight $W$ is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height $h$ from the ground, midway between ...

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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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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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GATE2019 ME-1: 38
A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the member BC is __________

A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the m...

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GATE2019 ME-1: 39
Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young's modulus $E=200 \: GPa$. This straight beam was bent in such a way that the two ends meets, to form a ... $MPa$.

Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young’s modulus $E=200 \: GPa$. This straight beam was ...

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GATE2019 ME-1: 40
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{-6} K^{-1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.

Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The You...

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GATE2019 ME-1: 41
In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head motion, at failure, was $15 \: mm$. The compliance of the UTM is constant and is given $5 \times 10^{-8} \: m/N$. The strain at failure in the sample is ______$\%$

In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head...

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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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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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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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GATE ME 2012 | Question: 49
Two steel truss members, AC and BC, each having cross sectional area of $100 mm^2$, are subjected to a horizontal force F as shown in the figure. All the joints are hinged. The maximum force F in kN that can be applied at $C$ such that the axial stress in any of the truss members DOES NOT exceed $100$ MPa is $8.17$ $11.15$ $14.14$ $22.30$

Two steel truss members, AC and BC, each having cross sectional area of $100 mm^2$, are subjected to a horizontal force F as shown in the figure. All the joints are hinge...

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GATE ME 2012 | Question: 48
Two steel truss members, AC and BC, each having cross sectional area of $100 mm^2$, are subjected to a horizontal force $F$ as shown in the figure. All the joints are hinged. If $F=1$ kN. the magnitude of the vertical reaction force developed at the point B in kN is $0.63$ $0.32$ $1.26$ $1.46$

Two steel truss members, AC and BC, each having cross sectional area of $100 mm^2$, are subjected to a horizontal force $F$ as shown in the figure. All the joints are hin...

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GATE ME 2012 | Question: 44
A force of $400$ N is applied to the brake drum of $0.5$ m diameter in a band-brake system as shown in the figure, where the wrapping angle is $180^{\circ}$. If the coefficient of friction between the drum and the band is $0.25$, the braking torque applied, in N.m is $100.6$ $54.4$ $22.1$ $15.7$

A force of $400$ N is applied to the brake drum of $0.5$ m diameter in a band-brake system as shown in the figure, where the wrapping angle is $180^{\circ}$. If the coeff...

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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: 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: 33
A concentrated mass $m$ is attached at the centre of the rod of length $2L$ as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of stiffness $k$. For every small amplitude of vibration, neglecting the weights of the rod and spring, the undamped ... $\sqrt{\dfrac{2k}{m}} \\$ $\sqrt{\dfrac{k}{2m}} \\$ $\sqrt{\dfrac{4k}{m}}$

A concentrated mass $m$ is attached at the centre of the rod of length $2L$ as shown in the figure. The rod is kept in a horizontal equilibrium position by a spring of st...

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GATE ME 2012 | Question: 32
A fillet welded joint is subjected to transverse loading $F$ as shown in the figure. Both legs of the fillets are of $10$ mm size and the weld length is $30$ mm. If the allowable shear stress of the weld is $94$ MPa, considering the minimum throat area of the weld, the maximum allowable transverse load in kN is $14.44$ $17.92$ $19.93$ $22.16$

A fillet welded joint is subjected to transverse loading $F$ as shown in the figure. Both legs of the fillets are of $10$ mm size and the weld length is $30$ mm. If the a...

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GATE ME 2012 | Question: 23
For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is $1$ $2$ $4$ $8$

For a long slender column of uniform cross section, the ratio of critical buckling load for the case with both ends clamped to the case with both ends hinged is$1$$2$$4$$...

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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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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 2012 | Question: 20
In the mechanism given below, if the angular velocity of the eccentric circular disc is $1$ rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is $0.05$ $0.1$ $5.0$ $10.0$

In the mechanism given below, if the angular velocity of the eccentric circular disc is $1$ rad/s, the angular velocity (rad/s) of the follower link for the instant shown...

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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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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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GATE2018-1-54
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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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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GATE2018-1-41
A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45$^{\circ}$ and force of $40$ N is acting towards the left on the slider. The length of the crank is $30$ mm and the connecting rod is $70$ mm. ... inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is ______ (correct to two decimal places)

A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45$^{\circ}$ and force of $40$ N is acting towards the left on the slider. The length...

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GATE2018-1-40
A machine of mass $m=200 \: kg$ is supported on two mounts, each of stiffness $k=10 \: kN/m$. The machine is subjected to an external force (in $N$) $F(t) = 50 \cos 5t$. Assuming only vertical translatory motion, the magnitude of the dynamic force (in $N$) transmitted from each mount to the ground is _________ (correct to two decimal places).

A machine of mass $m=200 \: kg$ is supported on two mounts, each of stiffness $k=10 \: kN/m$. The machine is subjected to an external force (in $N$) $F(t) = 50 \cos 5t$. ...

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GATE2018-1-32
A self-aligning ball bearing has a basic dynamic load rating $(C_{10}$, for $10^6$ revolutions) of $35$ kN. If the equivalent radial load on the bearing is $45$ kN, the expected life (in $10^6$ revolutions) is below $0.5$ $0.5$ to $0.8$ $0.8$ to $1.0$ above $1.0$

A self-aligning ball bearing has a basic dynamic load rating $(C_{10}$, for $10^6$ revolutions) of $35$ kN. If the equivalent radial load on the bearing is $45$ kN, the e...

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GATE2018-1-31
A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta = 30^{\circ}$ as shown in the figure. The glue used at the interface fails is Criterion 1: the maximum normal stress exceeds $2.5$ MPa Criterion 2: the ... fails only because of criterion $1$ fails only because of criterion $2$ fails because of both criterion $1$ and $2$ does not fail

A carpenter glues a pair of cylindrical wooden logs by bonding their end faces at an angle of $\theta = 30^{\circ}$ as shown in the figure.The glue used at the interface ...

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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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GATE2018-1-29
The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is $10$ kPa, then the normal stress $\sigma_y$ (in kPa) is $9.45$ $18.88$ $37.78$ $75.50$

The state of stress at a point, for a body in plane stress, is shown in the figure below. If the minimum principal stress is $10$ kPa, then the normal stress $\sigma_y$ (...

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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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GATE2018-1-21
If the wire diameter of a compressive helical spring is increased by $2 \%$, the change in spring stiffness (in $\%$) is _____ (correct to two decimal places)

If the wire diameter of a compressive helical spring is increased by $2 \%$, the change in spring stiffness (in $\%$) is _____ (correct to two decimal places)

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GATE2018-1-20
A four bar mechanism is made up of links of length $100$, $200$, $300$ and $350$ mm. If the $350$ mm link is fixed, the number of links that can rotate fully is _________

A four bar mechanism is made up of links of length $100$, $200$, $300$ and $350$ mm. If the $350$ mm link is fixed, the number of links that can rotate fully is _________...

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