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

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GATE2017 ME-1: 14
A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $r(t)=t^{2}, \theta (t)=t$, where $t$ is time. The Kinetic energy of the particle at time $t=2$ is $4$ $12$ $16$ $24$

A particle of unit mass is moving on a plane. Its trajectory, in polar coordinates, is given by $r(t)=t^{2}, \theta (t)=t$, where $t$ is time. The Kinetic energy of the p...

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GATE2017 ME-1: 13
The Poisson's ratio for a perfectly incompressible linear elastic material is $1$ $0.5$ $0$ Infinity

The Poisson's ratio for a perfectly incompressible linear elastic material is$1$$0.5$$0$Infinity

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GATE2016-3-50
In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultimate shear strength is $80$ $MPa$. The force required to punch the hole (in $kN$) is __________

In a sheet metal of $2$ $mm$ thickness a hole of $10$ $mm$ diameter needs to be punched. The yield strength in tension of the sheet material is $100$ $MPa$ and its ultima...

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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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GATE2016-3-37
A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of the amplitude of steady state response to the static deflection of the spring is __________

A single degree of freedom spring-mass system is subjected to a harmonic force of constant amplitude. For an excitation frequency of $\sqrt{\dfrac{3k}{m}}$, the ratio of ...

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GATE2016-3-36
Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses $m_1$ is attached to the opposite sides of the shaft in the vertical plane as shown in figure. Consider $m=1 \: kg$, $e=50 \: mm$, $e_1=20 \: mm$ ... $a=2 \: m$ and $a_1 = 2.5 \: m$. For the system to be dynamically balanced, $m_1$ should be ________ $kg$.

Two masses m are attached to opposite sides of a rigid rotating shaft in the vertical plane. Another pair of equal masses $m_1$ is attached to the opposite sides of the s...

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GATE2016-3-35
A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the right end is $\dfrac{wL}{2} \\$ $\dfrac{3wL}{8} \\$ $\dfrac{wL}{4} \\$ $\dfrac{wL}{8}$

A beam of length $L$ is carrying a uniformly distributed load w per unit length. The flexural rigidity of the beam is $EI$. The reaction at the simple support at the righ...

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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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GATE2016-3-33
A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Young’s modulus $E=200 \: GPa$ .The deformed shape is a square of dimension $L− 2\delta$. If $L = 2 \: m$ and $\delta=0.001 \: m$, the Poisson’s ratio of the plate material is __________

A square plate of dimension $L \times L$ is subjected to a uniform pressure load $p=250 \: MPa$ on its edges as shown in the figure. Assume plane stress conditions. The Y...

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GATE2016-3-32
A rigid rod $(AB)$ of length $L=\sqrt{2} \: m$ is undergoing translational as well as rotational motion in the $x-y$ plane (see the figure). The point $A$ has the velocity $V_1=\hat{i}+2\hat{j} \: m/s$. The end B is constrained to move only along the $x$ direction. The magnitude of the velocity $V_2$ (in $m/s$) at the end B is __________

A rigid rod $(AB)$ of length $L=\sqrt{2} \: m$ is undergoing translational as well as rotational motion in the $x-y$ plane (see the figure). The point $A$ has the velocit...

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GATE2016-3-31
A circular disc of radius $100 \: mm$ and mass $1 \: kg$, initially at rest at position $A$, rolls without slipping down a curved path as shown in figure. The speed $v$ of the disc when it reaches position $B$ is _________ $m/s$. Acceleration due to gravity $g = 10 \: m/s^2$.

A circular disc of radius $100 \: mm$ and mass $1 \: kg$, initially at rest at position $A$, rolls without slipping down a curved path as shown in figure. The speed $v$ o...

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GATE2016-3-30
An inextensible massless string goes over a frictionless pulley. Two weights of $100$ $N$ and $200$ $N$ are attached to the two ends of the string. The weights are released from rest, and start moving due to gravity. The tension in the string (in $N$) is __________

An inextensible massless string goes over a frictionless pulley. Two weights of $100$ $N$ and $200$ $N$ are attached to the two ends of the string. The weights are releas...

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GATE2016-3-20
Engineering strain of a mild steel sample is recorded as $0.100\%$. The true strain is $0.010\%$ $0.055\%$ $0.099\%$ $0.101\%$

Engineering strain of a mild steel sample is recorded as $0.100\%$. The true strain is$0.010\%$$0.055\%$$0.099\%$$0.101\%$

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GATE2016-3-15
Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the figure, where $k_A$ , $k_B$ denote the respective thermal conductivities. Using the data as given in the figure, the interface temperature $T_2$ (in $^\circ C$) is __________

Steady one-dimensional heat conduction takes place across the faces $1$ and $3$ of a composite slab consisting of slabs $A$ and $B$ in perfect contact as shown in the fig...

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GATE2016-3-12
Which of the bearings given below SHOULD NOT be subjected to a thrust load? Deep groove ball bearing Angular contact ball bearing Cylindrical (straight) roller bearing Single row tapered roller bearing

Which of the bearings given below SHOULD NOT be subjected to a thrust load?Deep groove ball bearingAngular contact ball bearingCylindrical (straight) roller bearingSingle...

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GATE2016-3-11
The static deflection of a spring under gravity, when a mass of $1 \:kg$ is suspended from it, is $1 \: mm$. Assume the acceleration due to gravity $g =10 \: m/s^2$. The natural frequency of this spring-mass system (in $rad/s$) is_____________

The static deflection of a spring under gravity, when a mass of $1 \:kg$ is suspended from it, is $1 \: mm$. Assume the acceleration due to gravity $g =10 \: m/s^2$. The ...

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GATE2016-3-10
The number of degrees of freedom in a planar mechanism having n links and j simple hinge joints is $3 ( n− 3) − 2j$ $3(n − 1) − 2j$ $3n − 2j$ $2j − 3n + 4$

The number of degrees of freedom in a planar mechanism having n links and j simple hinge joints is$3 ( n− 3) − 2j$$3(n − 1) − 2j$$3n − 2j$$2j − 3n + 4$

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GATE2016-3-9
A rigid link $PQ$ is undergoing plane motion as shown in the figure ($V_P$ and $V_Q$ are non-zero). $V_{QP}$ is the relative velocity of point $Q$ with respect to point $P$. Which one of the following is TRUE? $V_{QP}$ ... $Q$ $V_{QP}$ has only one component directed from $Q$ to $P$ $V_{QP}$ has only one component perpendicular to $PQ$

A rigid link $PQ$ is undergoing plane motion as shown in the figure ($V_P$ and $V_Q$ are non-zero). $V_{QP}$ is the relative velocity of point $Q$ with respect to point $...

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GATE2016-3-8
T he state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b). The components $(\tau _{xx},\tau_{yy},\tau _{xy})$ are given by $(p/\sqrt{2},-p/\sqrt{2},0)$ $(0,0,p)$ $(p,-p,p/\sqrt{2})$ $(0,0,p/\sqrt{2})$

T he state of stress at a point on an element is shown in figure (a). The same state of stress is shown in another coordinate system in figure (b).The components $(\tau _...

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GATE2016-3-7
The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $I_1$, while the circular cross-section has flexural rigidity $I_2$. Both sections have the same cross-sectional area. The ratio $I_1/I_2$ is $1/ \pi \\$ $2/ \pi \\$ $ \pi/3 \\$ $ \pi/6 $

The cross-sections of two solid bars made of the same material are shown in the figure. The square cross-section has flexural (bending) rigidity $I_1$, while the circular...

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GATE2016-3-6
A force F is acting on a bent bar which is clamped at one end as shown in the figure. The CORRECT free body diagram is

A force F is acting on a bent bar which is clamped at one end as shown in the figure.The CORRECT free body diagram is

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GATE2016-2-38
In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $50$ $MPa$ and $150$ $MPa$, respectively. The endurance, yield, and the ultimate strengths of the material are $200$ $MPa$, $300$ $MPa$ and $400$ $MPa$, respectively. ... safety using modified Goodman criterion is $\dfrac{3}{2} \\$ $\dfrac{8}{5} \\$ $\dfrac{12}{7} \\$ $2$

In a structural member under fatigue loading, the minimum and maximum stresses developed at the critical point are $50$ $MPa$ and $150$ $MPa$, respectively. The endurance...

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GATE2016-2-37
The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. The spring constant $k$ is $1500$ $N/m$. If there is no slipping of the rope over the pulley, the natural frequency of the system is_____________ $rad/s$.

The system shown in the figure consists of block A of mass $5$ $kg$ connected to a spring through a massless rope passing over pulley B of radius $r$ and mass $20$ $kg$. ...

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GATE2016-2-36
The rod $AB$, of length $1$ $m$, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along $QP$ and $QR$. If the velocity $VA$ of the slider at $A$ is $2$ $m/s$, the velocity of the midpoint of the rod at this instant is ___________ $m/s$.

The rod $AB$, of length $1$ $m$, shown in the figure is connected to two sliders at each end through pins. The sliders can slide along $QP$ and $QR$. If the velocity $VA$...

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GATE2016-2-34
In the figure, the load $P=1 \: N$, length $L=1 \: m$, Young’s modulus $E=70 \: GPa$, and the cross-section of the links is a square with dimension $10 \: mm \times 10 \: mm$. All joints are pin joints. The stress (in $Pa$) in the link $AB$ is ___________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

In the figure, the load $P=1 \: N$, length $L=1 \: m$, Young’s modulus $E=70 \: GPa$, and the cross-section of the links is a square with dimension $10 \: mm \times 10 ...

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GATE2016-2-33
A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is given by $w=\dfrac{-Mx}{12EIL}(L-x)(x+c)$ where $E$ is the Young's modulus, $I$ is the area moment ... is a constant (to be determined) . The slope at the center $x$ = $0$ is $ML/(2EI)$ $ML/(3EI)$ $ML/(6EI)$ $ML/(12EI)$

A simply supported beam of length $2L$ is subjected to a moment $M$ at the mid-point $x = 0$ as shown in the figure. The deflection in the domain $0 \leq x \leq L$ is giv...

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GATE2016-2-32
A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends as shown in the figure. The shear modulus for the cylinder is $G$ and the Young’s modulus is $E$. The vertical deflection at point A is $PL^3/(\pi R^4G)$ $PL^3/(\pi R^4E)$ $2PL^3/(\pi R^4E)$ $4PL^3/(\pi R^4G)$

A rigid horizontal rod of length $2L$ is fixed to a circular cylinder of radius $R$ as shown in the figure. Vertical forces of magnitude $P$ are applied at the two ends a...

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GATE2016-2-31
A system of particles in motion has mass center $G$ as shown in the figure. The particle $i$ has mass $m_i$ and its position with respect to a fixed point $O$ is given by the position vector $r_i$. The position of the particle with respect to $G$ ... $\sum _i\rho _i\times m_i\ddot{r_i}$ $\sum _ir _i\times m_i\ddot{r_i}$ $\sum _i\rho _i\times m_i\ddot{\rho _i}$

A system of particles in motion has mass center $G$ as shown in the figure. The particle $i$ has mass $m_i$ and its position with respect to a fixed point $O$ is given by...

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GATE2016-2-30
A mass of $2000$ $kg$ is currently being lowered at a velocity of $2$ $m/s$ from the drum as shown in the figure. The mass moment of inertia of the drum is $150$ $kg$-$m^2$. On applying the brake, the mass is brought to rest in a distance of $0.5$ $m$. The energy absorbed by the brake (in $kJ$) is __________

A mass of $2000$ $kg$ is currently being lowered at a velocity of $2$ $m/s$ from the drum as shown in the figure. The mass moment of inertia of the drum is $150$ $kg$-$m^...

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GATE2016-2-23
The value of true strain produced in compressing a cylinder to half its original length is $0.69$ $-0.69$ $0.5$ $-0.5$

The value of true strain produced in compressing a cylinder to half its original length is$0.69$$-0.69$$0.5$$-0.5$

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GATE2016-2-12
For the brake shown in the figure, which one of the following is TRUE? Self energizing for clockwise rotation of the drum Self energizing for anti-clockwise rotation of the drum Self energizing for rotation in either direction of the drum Not of the self energizing type

For the brake shown in the figure, which one of the following is TRUE?Self energizing for clockwise rotation of the drumSelf energizing for anti-clockwise rotation of the...

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GATE2016-2-11
A machine element XY, fixed at end X, is subjected to an axial load P, transverse load F, and a twisting moment T at its free end Y. The most critical point from the strength point of view is a point on the circumference at location Y a point at the center at location Y a point on the circumference at location X a point at the center at location X

A machine element XY, fixed at end X, is subjected to an axial load P, transverse load F, and a twisting moment T at its free end Y. The most critical point from the stre...

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GATE2016-2-10
A single degree of freedom mass-spring-viscous damper system with mass $m$, spring constant $k$ and viscous damping coefficient $q$ is critically damped. The correct relation among $m$, $k$, and $q$ is $q=\sqrt{2km} \\$ $q=2\sqrt{km} \\$ $q=\sqrt{\dfrac{2k}{m}} \\$ $q=2\sqrt{\dfrac{k}{m}}$

A single degree of freedom mass-spring-viscous damper system with mass $m$, spring constant $k$ and viscous damping coefficient $q$ is critically damped. The correct rela...

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GATE2016-2-9
The forces $F_1$ and $F_2$ in a brake band and the direction of rotation of the drum are as shown in the figure. The coefficient of friction is $0.25$. The angle of wrap is $3\pi /2$ radians. It is given that $R$ = $1$ $m$ and $F_2$ = $1$ $N$. The torque (in $N$-$m$) exerted on the drum is _________

The forces $F_1$ and $F_2$ in a brake band and the direction of rotation of the drum are as shown in the figure. The coefficient of friction is $0.25$. The angle of wrap ...

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GATE2016-2-8
A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is $0.25$ $0.50$ $1.0$ $2.0$

A thin cylindrical pressure vessel with closed-ends is subjected to internal pressure. The ratio of circumferential (hoop) stress to the longitudinal stress is$0.25$$0.50...

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GATE2016-2-7
A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is $2.0$ $1.0$ $0.5$ $0$

A shaft with a circular cross-section is subjected to pure twisting moment. The ratio of the maximum shear stress to the largest principal stress is$2.0$$1.0$$0.5$$0$

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GATE2016-1-52
A $300$ $mm$ thick slab is being cold rolled using roll of $600$ $mm$ diameter. If the coefficient of friction is $0.08$, the maximum possible reduction (in $mm$) is __________

A $300$ $mm$ thick slab is being cold rolled using roll of $600$ $mm$ diameter. If the coefficient of friction is $0.08$, the maximum possible reduction (in $mm$) is ____...

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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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GATE2016-1-48
A hypothetical engineering stress-strain curve shown in the figure has three straight lines $PQ, QR, RS$ with coordinates P$(0,0)$, Q$(0.2,100)$, R$(0.6,140)$ and S$(0.8,130)$. $'Q'$ is the yield point, $'R'$ is the UTS point and $'S'$ the fracture point. The toughness of the material (in $MJ/m^3$) is __________

A hypothetical engineering stress-strain curve shown in the figure has three straight lines $PQ, QR, RS$ with coordinates P$(0,0)$, Q$(0.2,100)$, R$(0.6,140)$ and S$(0.8,...

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GATE2016-1-38
The principal stresses at a point inside a solid object are $\sigma _1$ = $100$ $MPa$, $\sigma _2$ = $100$ $MPa$ and $\sigma _3$ = $0$ $MPa$. The yield strength of the material is $200$ $MPa$. The factor of safety calculated using Tresca (maximum shear stress) theory is ... one of the following relations is TRUE? $n_T=(\sqrt{3}/2)n_V$ $n_T=(\sqrt{3})n_V$ $n_T=n_V$ $n_V=(\sqrt{3})n_T$

The principal stresses at a point inside a solid object are $\sigma _1$ = $100$ $MPa$, $\sigma _2$ = $100$ $MPa$ and $\sigma _3$ = $0$ $MPa$. The yield strength of the ma...

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