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

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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: 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: 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: 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: 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: 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 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: 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: 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: 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: 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: 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: 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: 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: 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: 33
The damping ratio of a single degree of freedom spring-mass-damper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is _______

The damping ratio of a single degree of freedom spring-mass-damper system with mass of $1 kg$, stiffness $100 N/m$ and viscous damping coefficient of $25 N.s/m$ is ______...

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GATE Mechanical 2014 Set 3 | Question: 32
Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-point. The ratio of the maximum shear stress to the maximum bending stress in the beam is $0.02$ $0.10$ $0.05$ $0.01$

Consider a simply supported beam of length, $50h$, with a rectangular cross-section of depth, $h$, and width, $2h$. The beam carries a vertical point load, P, at its mid-...

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GATE Mechanical 2014 Set 3 | Question: 31
A body of mass (M) $10$ $kg$ is initially stationary on a $45^{\circ}$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the plane is $0.5$. The body slides down the plane and attains a velocity of $20 m/s$. The distance traveled (in meter) by the body along the plane is _______

A body of mass (M) $10$ $kg$ is initially stationary on a $45^{\circ}$ inclined plane as shown in figure. The coefficient of dynamic friction between the body and the pla...

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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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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: 12
Consider a long cylindrical tube of inner and outer radii, $r_i$ and $r_o$ , respectively, length, $L$ and thermal conductivity, $k$. Its inner and outer surfaces are maintained at $T_i$ and $T_o$ , respectively ( $T_i > T_o$ ). Assuming one-dimensional steady ... $\dfrac{1}{4\pi kL}\ln \bigg (\dfrac{r_o}{r_i} \bigg )$

Consider a long cylindrical tube of inner and outer radii, $r_i$ and $r_o$ , respectively, length, $L$ and thermal conductivity, $k$. Its inner and outer surfaces are mai...

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GATE Mechanical 2014 Set 3 | Question: 11
Gear $2$ rotates at $1200$ $rpm$ in counter clockwise direction and engages with Gear $3$. Gear $3$ and Gear $4$ are mounted on the same shaft. Gear $5$ engages with Gear $4$. The numbers of teeth on Gears $2$, $3$, $4$ ... angular speed of Gear $5$ is $300$ $rpm$ counterclockwise $300$ $rpm$ clockwise $4800$ $rpm$ counterclockwise $4800$ $rpm$ clockwise

Gear $2$ rotates at $1200$ $rpm$ in counter clockwise direction and engages with Gear $3$. Gear $3$ and Gear $4$ are mounted on the same shaft. Gear $5$ engages with Gear...

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GATE Mechanical 2014 Set 3 | Question: 10
Which one of following is NOT correct? Intermediate principal stress is ignored when applying the maximum principal stress theory The maximum shear stress theory gives the most accurate results amongst all the failure theories As per ... the maximum distortion energy theory, failure occurs when the distortion energy per unit volume exceeds a critical value

Which one of following is NOT correct?Intermediate principal stress is ignored when applying the maximum principal stress theoryThe maximum shear stress theory gives the ...

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GATE Mechanical 2014 Set 3 | Question: 9
A mass $m_1$ of $100$ $kg$ traveling with a uniform velocity of $5$ $m/s$ along a line collides with a stationary mass $m_2$ of $1000$ $kg$. After the collision, both the masses travel together with the same velocity. The coefficient of restitution is $0.6$ $0.1$ $0.01$ $0$

A mass $m_1$ of $100$ $kg$ traveling with a uniform velocity of $5$ $m/s$ along a line collides with a stationary mass $m_2$ of $1000$ $kg$. After the collision, both the...

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GATE Mechanical 2014 Set 3 | Question: 8
Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to the exciting force is $0$ $45$ $90$ $135$

Consider a single degree-of-freedom system with viscous damping excited by a harmonic force. At resonance, the phase angle (in degree) of the displacement with respect to...

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GATE Mechanical 2014 Set 3 | Question: 7
Two solid circular shafts of radii $R_1$ and $R_2$ are subjected to same torque. The maximum shear stresses developed in the two shafts are $\tau _1$ and $\tau _2$. If $R_1$/ $R_2$=$2$, then $\tau _2/\tau _1$ is _______

Two solid circular shafts of radii $R_1$ and $R_2$ are subjected to same torque. The maximum shearstresses developed in the two shafts are $\tau _1$ and $\tau _2$. If $R_...

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GATE Mechanical 2014 Set 3 | Question: 6
A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is $100$ $MPa$. If the yield, ultimate and corrected endurance strength of the shaft material are $300$ $MPa$, $500$ $MPa$ and $200$ $MPa$, respectively, then the factor of safety for the shaft is _______

A rotating steel shaft is supported at the ends. It is subjected to a point load at the center. The maximum bending stress developed is $100$ $MPa$. If the yield, ultimat...

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GATE Mechanical 2014 Set 2 | Question: 55
A rectangular hole of size $100$ $mm \times 50$ $mm$ is to be made on a $5$ $mm$ thick sheet of steel having ultimate tensile strength and shear strength of $500$ $MPa$ and $300$ $MPa$, respectively. The hole is made by punching process. Neglecting the effect of clearance, the punching force (in $kN$) is $300$ $450$ $600$ $750$

A rectangular hole of size $100$ $mm \times 50$ $mm$ is to be made on a $5$ $mm$ thick sheet of steel having ultimate tensile strength and shear strength of $500$ $MPa$ a...

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GATE Mechanical 2014 Set 2 | Question: 40
A spur pinion of pitch diameter $50$ $mm$ rotates at $200$ $rad/s$ and transmits $3 kW$ power. The pressure angle of the tooth of the pinion is $20^\circ$. Assuming that only one pair of the teeth is in contact, the total force (in newton) exerted by a tooth of the pinion on the tooth on a mating gear is _______

A spur pinion of pitch diameter $50$ $mm$ rotates at $200$ $rad/s$ and transmits $3 kW$ power. The pressure angle of the tooth of the pinion is $20^\circ$. Assuming that ...

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GATE Mechanical 2014 Set 2 | Question: 39
A rigid link $PQ$ of length $2$ $m$ rotates about the pinned end $Q$ with a constant angular acceleration of $12$ $rad$/$s^2$. When the angular velocity of the link is $4$ $rad$/$s$, the magnitude of the resultant acceleration (in $m$/$s^2$) of the end P is _______

A rigid link $PQ$ of length $2$ $m$ rotates about the pinned end $Q$ with a constant angular acceleration of $12$ $rad$/$s^2$. When the angular velocity of the link is $4...

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GATE Mechanical 2014 Set 2 | Question: 38
Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of the following statements is true? $I$ yields after $II$ $II$ yields after $I$ Both yield simultaneously Nothing can be said about their relative yielding

Consider the two states of stress as shown in configurations I and II in the figure below. From the standpoint of distortion energy (von-Mises) criterion, which one of th...

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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 Mechanical 2014 Set 2 | Question: 36
A truck accelerates up a $10^0$ incline with a crate of $100$ $kg$. Value of static coefficient of friction between the crate and the truck surface is $0.3$. The maximum value of acceleration (in $m$/$s^2$) of the truck such that the crate does not slide down is _______

A truck accelerates up a $10^0$ incline with a crate of $100$ $kg$. Value of static coefficient of friction between the crate and the truck surface is $0.3$. The maximum ...

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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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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: 33
Consider a flywheel whose mass $M$ is distributed almost equally between a heavy, ring-like rim of radius $R$ and a concentric disk-like feature of radius $R/2$. Other parts of the flywheel, such as spokes, etc, have negligible mass. The best ... for $α$, if the moment of inertia of the flywheel about its axis of rotation is expressed as $αMR^2$, is _______

Consider a flywheel whose mass $M$ is distributed almost equally between a heavy, ring-like rim of radius $R$ and a concentric disk-like feature of radius $R/2$. Other pa...

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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: 31
A cantilever beam of length, $L$, with uniform cross-section and flexural rigidity, $EI$, is loaded uniformly by a vertical load, $w$ per unit length. The maximum vertical deflection of the beam is given by $\dfrac{wL^4}{8EI} \\$ $\dfrac{wL^4}{16EI} \\$ $\dfrac{wL^4}{4EI} \\$ $\dfrac{wL^4}{24EI}$

A cantilever beam of length, $L$, with uniform cross-section and flexural rigidity, $EI$, is loaded uniformly by a vertical load, $w$ per unit length. The maximum vertica...

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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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GATE Mechanical 2014 Set 2 | Question: 24
The relationship between true strain ($\epsilon _T$) and engineering strain ($\epsilon _E$) in a uniaxial tension test is given as $\epsilon _E=ln(1+\epsilon _T)$ $\epsilon _E=ln(1-\epsilon _T)$ $\epsilon _T=ln(1+\epsilon _E)$ $\epsilon _T=ln(1-\epsilon _E)$

The relationship between true strain ($\epsilon _T$) and engineering strain ($\epsilon _E$) in a uniaxial tension test is given as$\epsilon _E=ln(1+\epsilon _T)$$\epsilon...

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