Recent questions in Applied Mechanics and Design / GO Mechanical

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GATE2018-2-25
A ball is dropped from rest from a height of $1 \: m$ in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring the curved portion), the total distance travelled (in $m$) by the ball is _____ (correct to two decimal places)

A ball is dropped from rest from a height of $1 \: m$ in a frictionless tube as shown in the figure. If the tube profile is approximated by two straight lines (ignoring t...

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GATE2018-2-21
Fatigue life of a material for a fully reversed loading condition is estimated from $\sigma_a=1100N^{-0.15}$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ is the failure life in cycles. The maximum allowable stress amplitude (in $MPa$) for a life of $1 \times 10^5$ cycles under the same loading condition is ________ (correct to two decimal places).

Fatigue life of a material for a fully reversed loading condition is estimated from $$\sigma_a=1100N^{-0.15}$$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ ...

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GATE2018-2-20
A hollow circular shaft of inner radius $10 \: mm$ outer radius $20 \: mm$ length $1 \: m$ is to be used as a torsional spring. If the shear modulus of the material of the shaft is $150 \: GPa$, the torsional stiffness of the shaft (in $kN-m/rad$) is ________ (correct to two decimal places).

A hollow circular shaft of inner radius $10 \: mm$ outer radius $20 \: mm$ length $1 \: m$ is to be used as a torsional spring. If the shear modulus of the material of th...

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GATE2018-2-8
Pre-tensioning of a bolted joint is used to strain harden the bolt head decrease stiffness of the bolted joint increase stiffness of the bolted joint prevent yielding of the thread root

Pre-tensioning of a bolted joint is used tostrain harden the bolt headdecrease stiffness of the bolted jointincrease stiffness of the bolted jointprevent yielding of the ...

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GATE2018-2-7
In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains underdamped. Which one of the following statements is ALWAYS ... will increase Transmissibility will decrease Time period of free oscillations will increase Time period of free oscillations will decrease

In a single degree of freedom underdamped spring-mass-damper system as shown in the figure, an additional damper is added in parallel such that the system still remains u...

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GATE2018-2-5
The minimum axial compressive load, $P$, required to initiate buckling for a pinned-pinned slender column with bending stiffness $EI$ and length $L$ is $P=\dfrac{\pi^2 EI}{4L^2} \\$ $P=\dfrac{\pi^2 EI}{L^2} \\$ $P=\dfrac{3\pi^2 EI}{4L^2} \\$ $P=\dfrac{4\pi^2 EI}{L^2}$

The minimum axial compressive load, $P$, required to initiate buckling for a pinned-pinned slender column with bending stiffness $EI$ and length $L$ is$P=\dfrac{\pi^2 EI}...

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GATE2018-2-6
A frictionless gear train is shown in the figure. The leftmost $12$-teeth gear is given a torque of $100 \: N-m$. The output torque from the $60$-teeth gear on the right in $N-m$ is $5$ $20$ $500$ $2000$

A frictionless gear train is shown in the figure. The leftmost $12$-teeth gear is given a torque of $100 \: N-m$. The output torque from the $60$-teeth gear on the right ...

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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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GATE2018-1-53
The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at point X. A force $F=100$ N is applied at the free end of the lever as shown. Given that the ... the shoe and the drum is $0.3$, the braking torque in (Nm) applied on the drum is _____ (correct to two decimal places)

The schematic of an external drum rotating clockwise engaging with a short shoe is shown in the figure. The shoe is mounted at point Y on a rigid lever XYZ hinged at poin...

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GATE2018-1-50
A bar is compressed to half to its original length. The magnitude of true strain produced in the deformed bar is __________ (correct to two decimal places)

A bar is compressed to half to its original length. The magnitude of true strain produced in the deformed bar is __________ (correct to two decimal places)

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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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GATE2018-1-39
A simply supported beam of width $100$ mm, height $200$ mm and length 4 m is carrying a uniformly distributed load of intensity $10 \: kN/m$. The maximum bending stress (in MPa) in the beam is _________ (correct to one decimal place)

A simply supported beam of width $100$ mm, height $200$ mm and length 4 m is carrying a uniformly distributed load of intensity $10 \: kN/m$. The maximum bending stress (...

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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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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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GATE2018-1-17
The number of atoms per unit cell and the number of slip systems, respectively, for a face-centered cubic (FCC) crystal are $3, 3$ $3, 12$ $4, 12$ $4, 48$

The number of atoms per unit cell and the number of slip systems, respectively, for a face-centered cubic (FCC) crystal are$3, 3$$3, 12$$4, 12$$4, 48$

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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: 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: 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: 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: 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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