Recent questions in Applied Mechanics and Design / GO Mechanical

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GATE2015-1-43
A machine element is subjected to the following bi-axial state of stress: $\sigma _x$ = $80$ $MPa$; $\sigma _y$ = 20 MPa; $\tau _{xy}$ = $40$ $MPa$. If the shear strength of the material is $100$ $MPa$, the factor of safety as per Tresca’s maximum shear stress theory is $1.0$ $2.0$ $2.5$ $3.3$

A machine element is subjected to the following bi-axial state of stress: $\sigma _x$ = $80$ $MPa$; $\sigma _y$ = 20 MPa; $\tau _{xy}$ = $40$ $MPa$. If the shear strength...

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GATE2015-1-44
A cantilever beam with flexural rigidity of $200$ $N.m^2$ is loaded as shown in the figure. The deflection (in $mm$) at the tip of the beam is _______

A cantilever beam with flexural rigidity of $200$ $N.m^2$ is loaded as shown in the figure. The deflection (in $mm$) at the tip of the beam is _______

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GATE2015-1-45
A precision instrument package $(m = 1 \: kg)$ needs to be mounted on a surface vibrating at $60 \: Hz$. It is desired that only $5\%$ of the base surface vibration amplitude be transmitted to the instrument. Assume that the isolation is designed with its natural ... $N/m$) of the required mounting pad is _____

A precision instrument package $(m = 1 \: kg)$ needs to be mounted on a surface vibrating at $60 \: Hz$. It is desired that only $5\%$ of the base surface vibration ampli...

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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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GATE2015-1-14
Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $\tau$ is applied on the crank as shown in the figure. Which of the following plots best resembles variation of crank angle, $\theta$ versus time

Consider a slider crank mechanism with nonzero masses and inertia. A constant torque $\tau$ is applied on the crank as shown in the figure. Which of the following plots b...

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GATE2015-1-15
Consider a stepped shaft subjected to a twisting moment applied at $B$ as shown in the figure. Assume shear modulus, $G$ = $77$ $GPa$. The angle of twist at $C$ (in degrees) is __________

Consider a stepped shaft subjected to a twisting moment applied at $B$ as shown in the figure. Assume shear modulus, $G$ = $77$ $GPa$. The angle of twist at $C$ (in degre...

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GATE2015-1-16
Two identical trusses support a load of $100$ $N$ as shown in the figure. The length of each truss is $1.0$ $m$; cross-sectional area is $200$ $mm^2$; Young’s modulus $E$ = $200$ $GPa$. The force in the truss $AB$ (in $N$) is _________

Two identical trusses support a load of $100$ $N$ as shown in the figure. The length of each truss is $1.0$ $m$; cross-sectional area is $200$ $mm^2$; Young’s modulus $...

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GATE2015-1-17
Consider a steel (Young’s modulus $E$ = $200 \: GPa$) column hinged on both sides. Its height is $1.0 \: m$ and cross-section is $10 \: mm \times 20$ $mm$. The lowest Euler critical buckling load (in $N$) is __________

Consider a steel (Young’s modulus $E$ = $200 \: GPa$) column hinged on both sides. Its height is $1.0 \: m$ and cross-section is $10 \: mm \times 20$ $mm$. The lowest E...

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GATE2015-1-19
Which one of the following is the most conservative fatigue failure criterion? Soderberg Modified Goodman ASME Elliptic Gerber

Which one of the following is the most conservative fatigue failure criterion?SoderbergModified GoodmanASME EllipticGerber

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GATE2015-1-20
Which one of the following types of stress-strain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, ($\sigma$ = stress and $\varepsilon$ = strain)?

Which one of the following types of stress-strain relationship best describes the behaviour of brittle materials, such as ceramics and thermosetting plastics, ($\sigma$ =...

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GATE Mechanical 2014 Set 4 | Question: 55
A butt weld joint is developed on steel plates having yield and ultimate tensile strength of $500$ $MPa$ and $700$ $MPa$, respectively. The thickness of the plates is $8$ $mm$ and width is $20$ $mm$. Improper selection of ... $mm$ depth along the weld. The maximum transverse tensile load (in $kN$) carrying capacity of the developed weld joint is _______

A butt weld joint is developed on steel plates having yield and ultimate tensile strength of $500$ $MPa$ and $700$ $MPa$, respectively. The thickness of the plates is $8$...

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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 4 | Question: 30
A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $100$ $MPa$. The yield and ultimate strengths of the shaft material in tension are $300$ $MPa$ and $450$ $MPa$, respectively. The factor of safety using maximum distortion energy (von-Mises) theory is _______

A shaft is subjected to pure torsional moment. The maximum shear stress developed in the shaft is $100$ $MPa$. The yield and ultimate strengths of the shaft material in t...

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GATE Mechanical 2014 Set 4 | Question: 31
A thin gas cylinder with an internal radius of $100$ $mm$ is subject to an internal pressure of $10$ $MPa$. The maximum permissible working stress is restricted to $100$ $MPa$. The minimum cylinder wall thickness (in $mm$) for safe design must be _______

A thin gas cylinder with an internal radius of $100$ $mm$ is subject to an internal pressure of $10$ $MPa$. The maximum permissible working stress is restricted to $100$ ...

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GATE Mechanical 2014 Set 4 | Question: 32
For the truss shown in the figure, the forces $F_1$ and $F_2$ are $9$ $kN$ and $3$ $kN$, respectively. The force (in $kN$) in the member QS is $11.25$ tension $11.25$ compression $13.5$ tension $13.5$ compression

For the truss shown in the figure, the forces $F_1$ and $F_2$ are $9$ $kN$ and $3$ $kN$, respectively. The force (in $kN$) in the member QS is$11.25$ tension$11.25$ compr...

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GATE Mechanical 2014 Set 4 | Question: 33
It is desired to avoid interference in a pair of spur gears having a $20^{\circ}$ pressure angle. With increase in pinion to gear speed ratio, the minimum number of teeth on the pinion increases decreases first increases and then decreases remains unchanged

It is desired to avoid interference in a pair of spur gears having a $20^{\circ}$ pressure angle. With increase in pinion to gear speed ratio, the minimum number of teeth...

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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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GATE Mechanical 2014 Set 4 | Question: 35
A bolt of major diameter $12$ $mm$ is required to clamp two steel plates. Cross sectional area of the threaded portion of the bolt is $84.3$ $mm^2$. The length of the threaded portion in grip is $30$ $mm$, while the length of ... Young's modulus of material is $200$ $GPa$. The effective stiffness (in $MN/m$) of the bolt in the clamped zone is_______

A bolt of major diameter $12$ $mm$ is required to clamp two steel plates. Cross sectional area of the threaded portion of the bolt is $84.3$ $mm^2$. The length of the thr...

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GATE Mechanical 2014 Set 4 | Question: 36
A frame is subjected to a load $P$ as shown in the figure. The frame has a constant flexural rigidity $EI$. The effect of axial load is neglected. The deflection at point $A$ due to the applied load $P$ is $\dfrac{1}{3}\dfrac{PL^3}{EI} \\$ $\dfrac{2}{3}\dfrac{PL^3}{EI} \\$ $\dfrac{PL^3}{EI} \\$ $\dfrac{4}{3}\dfrac{PL^3}{EI}$

A frame is subjected to a load $P$ as shown in the figure. The frame has a constant flexural rigidity $EI$. The effect of axial load is neglected. The deflection at point...

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GATE Mechanical 2014 Set 4 | Question: 37
A wardrobe (mass $100$ $kg$, height $4$ $m$, width $2$ $m$, depth $1$ $m$), symmetric about the $Y$-$Y$ axis, stands on a rough level floor as shown in the figure. A force $P$ ... and the wardrobe, respectively? $490.5$ and $0.5$ $981$ and $0.5$ $1000.5$ and $0.15$ $1000.5$ and $0.25$

A wardrobe (mass $100$ $kg$, height $4$ $m$, width $2$ $m$, depth $1$ $m$), symmetric about the $Y$-$Y$ axis, stands on a rough level floor as shown in the figure. A forc...

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GATE Mechanical 2014 Set 4 | Question: 38
Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figures. The moment of inertia (in $kg.m^2$) of the flywheel is _______

Torque and angular speed data over one cycle for a shaft carrying a flywheel are shown in the figures. The moment of inertia (in $kg.m^2$) of the flywheel is _______

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GATE Mechanical 2014 Set 4 | Question: 39
A single degree of freedom system has a mass of $2$ $kg$, stiffness $8$ $N/m$ and viscous damping ratio $0.02$. The dynamic magnification factor at an excitation frequency of $1.5$ $rad/s$ is _______

A single degree of freedom system has a mass of $2$ $kg$, stiffness $8$ $N/m$ and viscous damping ratio $0.02$. The dynamic magnification factor at an excitation frequenc...

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GATE Mechanical 2014 Set 4 | Question: 4
A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of $Rs.$ $500$ and a standard deviation of $Rs$. $50$. The percentage of savings account holders, who maintain an average daily balance more than $Rs$. $500$ is _______

A nationalized bank has found that the daily balance available in its savings accounts follows a normal distribution with a mean of $Rs.$ $500$ and a standard deviation o...

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GATE Mechanical 2014 Set 4 | Question: 6
In a statically determinate plane truss, the number of joints $(j)$ and the number of members $(m)$ are related by $j = 2m – 3$ $m = 2j + 1$ $m = 2j – 3$ $m = 2j − 1$

In a statically determinate plane truss, the number of joints $(j)$ and the number of members $(m)$ are related by$j = 2m – 3$$m = 2j + 1$$m = 2j – 3$$m = 2j − 1$

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GATE Mechanical 2014 Set 4 | Question: 7
If the Poisson's ratio of an elastic material is $0.4$, the ratio of modulus of rigidity to Young's modulus is _______

If the Poisson's ratio of an elastic material is $0.4$, the ratio of modulus of rigidity to Young's modulus is _______

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GATE Mechanical 2014 Set 4 | Question: 8
Which one of the following is used to convert a rotational motion into a translational motion? Bevel gears Double helical gears Worm gears Rack and pinion gears

Which one of the following is used to convert a rotational motion into a translational motion?Bevel gearsDouble helical gearsWorm gearsRack and pinion gears

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GATE Mechanical 2014 Set 4 | Question: 9
The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic solid is _______

The number of independent elastic constants required to define the stress-strain relationship for an isotropic elastic solid is _______

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GATE Mechanical 2014 Set 4 | Question: 10
A point mass is executing simple harmonic motion with an amplitude of $10$ $mm$ and frequency of $4$ $Hz$. The maximum acceleration ($m/s^2$) of the mass is _______

A point mass is executing simple harmonic motion with an amplitude of $10$ $mm$ and frequency of $4$ $Hz$. The maximum acceleration ($m/s^2$) of the mass is _______

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GATE Mechanical 2014 Set 4 | Question: 11
Ball bearings are rated by a manufacturer for a life of $10^6$ revolutions. The catalogue rating of a particular bearing is $16$ $kN$. If the design load is $2$ $kN$, the life of the bearing will be $p\times 10^6$ revolutions, where $p$ is equal to _______

Ball bearings are rated by a manufacturer for a life of $10^6$ revolutions. The catalogue rating of a particular bearing is $16$ $kN$. If the design load is $2$ $kN$, the...

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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 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: 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: 34
An annular disc has a mass $m$, inner radius $R$ and outer radius $2R$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$, the kinetic energy of the disc is $\dfrac{9}{16}mv^2 \\$ $\dfrac{11}{16}mv^2 \\$ $\dfrac{13}{16}mv^2 \\$ $\dfrac{15}{16}mv^2$

An annular disc has a mass $m$, inner radius $R$ and outer radius $2R$. The disc rolls on a flat surface without slipping. If the velocity of the center of mass is $v$, t...

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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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GATE Mechanical 2014 Set 3 | Question: 36
Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$, lying in the interval $0$ to $2 \pi$, is associated with the maximum translation of the follower during one full rotation of the cam rotating ... $x(t)$= $\dfrac{1}{2}$+$\cos t$ , $y(t)=\sin t$

Consider a rotating disk cam and a translating roller follower with zero offset. Which one of the following pitch curves, parameterized by $t$, lying in the interval $0$ ...

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GATE Mechanical 2014 Set 3 | Question: 37
A four-wheel vehicle of mass $1000 \: kg$ moves uniformly in a straight line with the wheels revolving at $10 \: rad/s$. The wheels are identical, each with a radius of $0.2 \: m$. Then a constant braking torque is applied to all the ... a uniform deceleration. For the vehicle to stop in $10 \: s$, the braking torque (in $N.m$) on each wheel is______

A four-wheel vehicle of mass $1000 \: kg$ moves uniformly in a straight line with the wheels revolving at $10 \: rad/s$. The wheels are identical, each with a radius of $...

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GATE Mechanical 2014 Set 3 | Question: 38
A slider-crank mechanism with crank radius $60$ $mm$ and connecting rod length $240$ $mm$ is shown in figure. The crank is rotating with a uniform angular speed of $10$ $rad/s$, counter clockwise. For the given configuration, the speed (in $m/s$) of the slider is _______

A slider-crank mechanism with crank radius $60$ $mm$ and connecting rod length $240$ $mm$ is shown in figure. The crank is rotating with a uniform angular speed of $10$ $...

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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 Mechanical 2014 Set 3 | Question: 24
The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table. ... $P-3, Q-4, R-1, S-5,T-2, U-6$ $P-4, Q-1, R-5, S-2,T-3, U-6$

The stress-strain curve for mild steel is shown in the figure given below. Choose the correct option referring to both figure and table.$\begin{array}{|l|l|}\hline \textb...

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GATE Mechanical 2014 Set 3 | Question: 30
A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $0.2$. The dimensions shown in the figure are in $mm$. The braking torque (in $N.m$) for the brake shoe is _______

A drum brake is shown in the figure. The drum is rotating in anticlockwise direction. The coefficient of friction between drum and shoe is $0.2$. The dimensions shown in ...

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