Recent questions in Applied Mechanics and Design / GO Mechanical

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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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GATE2016-3-10
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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GATE2016-3-11
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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GATE2016-3-12
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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GATE2016-2-38
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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GATE2016-2-30
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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GATE2016-2-31
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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GATE2016-2-32
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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GATE2016-2-33
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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GATE2016-2-34
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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GATE2016-2-36
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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GATE2016-2-37
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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GATE2016-2-23
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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GATE2016-2-7
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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GATE2016-2-8
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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GATE2016-2-9
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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GATE2016-2-10
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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GATE2016-2-11
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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GATE2016-2-12
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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GATE2016-1-48
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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GATE2016-1-51
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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GATE2016-1-52
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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GATE2016-1-32
A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respectively. For the deflection at $C$ to be zero, the ratio $\displaystyle{\frac{P}{F}}$ is ____________

A horizontal bar with a constant cross-section is subjected to loading as shown in the figure. The Young’s moduli for the sections $AB$ and $BC$ are $3E$ and $E$, respe...

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GATE2016-1-33
The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in $mm^4$) of this cross-section about its base is ________

The figure shows cross-section of a beam subjected to bending. The area moment of inertia (in $mm^4$) of this cross-section about its base is ________

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GATE2016-1-34
A simply-supported beam of length $3L$ is subjected to the loading shown in the figure. It is given that $P=1\: N$, $L=1\:m$ and Young's modulus $E=200\:GPa$. The cross-section is a square with dimension $10\:mm\times10\:mm$. The ... at a distance of $1.5L$ from the left end is _____________ (Indicate compressive stress by a negative sign and tensile stress by a positive sign.)

A simply-supported beam of length $3L$ is subjected to the loading shown in the figure.It is given that $P=1\: N$, $L=1\:m$ and Young’s modulus $E=200\:GPa$. The cross-...

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GATE2016-1-35
A slider crank mechanism with crank radius $200\:mm$ and connecting rod length $800\:mm$ is shown. The crank is rotating at $600\:rpm$ in the counterclockwise direction. In the configuration shown, the crank makes an angle of $90^\circ$ with the sliding ... $kN-m$) is __________

A slider crank mechanism with crank radius $200\:mm$ and connecting rod length $800\:mm$ is shown. The crank is rotating at $600\:rpm$ in the counterclockwise direction. ...

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GATE2016-1-36
In the gear train shown, gear $3$ is carried on arm $5$. Gear $3$ meshes with gear $2$ and gear $4$. The number of teeth on gear $2$, $3$, and $4$ are $60$, $20$, and $100$, respectively. If gear $2$ is fixed and gear $4$ ... the counterclockwise direction, the angular speed of arm $5$ (in $rpm$) is $166.7$ counterclockwise $166.7$ clockwise $62.5$ counterclockwise $62.5$ clockwise

In the gear train shown, gear $3$ is carried on arm $5$. Gear $3$ meshes with gear $2$ and gear $4$. The number of teeth on gear $2$, $3$, and $4$ are $60$, $20$, and $10...

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GATE2016-1-37
A solid disc with radius $a$ is connected to a spring at a point $d$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is free to roll without slipping on the ground. The mass of the disc is $M$ and the spring constant is $K$. The ... $\displaystyle{\sqrt{\frac{2K(a+d)^2}{Ma^2}}} \\$ $\displaystyle{\sqrt{\frac{K(a+d)^2}{Ma^2}}}$

A solid disc with radius $a$ is connected to a spring at a point $d$ above the center of the disc. The other end of the spring is fixed to the vertical wall. The disc is ...

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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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GATE2016-1-30
A block of mass $m$ rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and the block is $0.25$. The string can withstand a maximum force of $20$ $N$. The maximum value ... equilibrium is ____________ $kg$. Take $cos\theta$ and $sin \theta$ Acceleration due to gravity $g$ = $10$ $m$/$s^2$

A block of mass $m$ rests on an inclined plane and is attached by a string to the wall as shown in the figure. The coefficient of static friction between the plane and th...

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GATE2016-1-31
A two-member truss $PQR$ is supporting a load $W$. The axial forces in members $PQ$ and $QR$ are respectively $2W$ tensile and $\sqrt{3}W$ compressive $\sqrt{3}W$ tensile and $2W$ compressive $\sqrt{3}W$ compressive and $2W$ tensile $2W$ compressive and $\sqrt{3}W$ tensile

A two-member truss $PQR$ is supporting a load $W$. The axial forces in members $PQ$ and $QR$ are respectively$2W$ tensile and $\sqrt{3}W$ compressive$\sqrt{3}W$ tensile a...

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GATE2016-1-8
The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that $r_3>r_1$ and $r_4 > r_2$, and that the areas of the cross-sections are the same. $J_1$ and $J_2$ are the torsional rigidities of the bars on ... , respectively. The ratio $\displaystyle{\frac{J_2}{J_1}}$ is $>1$ $<0.5$ $=1$ between $0.5$ and $1$

The cross sections of two hollow bars made of the same material are concentric circles as shown in the figure. It is given that $r_3>r_1$ and $r_4 r_2$, and that the are...

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GATE2016-1-9
A cantilever beam having square cross-section of side $a$ is subjected to an end load. If $a$ is increased by $19\%$, the tip deflection decreases approximately by $19\%$ $29\%$ $41\%$ $50\%$

A cantilever beam having square cross-section of side $a$ is subjected to an end load. If $a$ is increased by $19\%$, the tip deflection decreases approximately by$19\%$$...

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GATE2016-1-10
A car is moving on a curved horizontal road of radius $100$ $m$ with a speed of $20$ $m/s$. The rotating masses of the engine have an angular speed of $100$ $rad/s$ in clockwise direction when viewed from the front of the car. The combined moment of inertia of the rotating masses is $10$ $kg$-$m^2$. The magnitude of the gyroscopic moment (in $N$-$m$) is __________

A car is moving on a curved horizontal road of radius $100$ $m$ with a speed of $20$ $m/s$. The rotating masses of the engine have an angular speed of $100$ $rad/s$ in cl...

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GATE2016-1-11
A single degree of freedom spring mass system with viscous damping has a spring constant of $10$ $kN/m$. The system is excited by a sinusoidal force of amplitude $100$ $N$. If the damping factor (ratio) is $0.25$, the amplitude of steady state oscillation at resonance is ________$mm$.

A single degree of freedom spring mass system with viscous damping has a spring constant of $10$ $kN/m$. The system is excited by a sinusoidal force of amplitude $100$ $N...

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GATE2016-1-12
The spring constant of a helical compression spring DOES NOT depend on coil diameter material strength number of active turns wire diameter

The spring constant of a helical compression spring DOES NOT depend oncoil diametermaterial strengthnumber of active turnswire diameter

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GATE2016-1-6
A rigid ball of weight $100$ $N$ is suspended with the help of a string. The ball is pulled by a horizontal force $F$ such that the string makes an angle of $30^o$ with the vertical. The magnitude of force $F$ (in $N$) is __________

A rigid ball of weight $100$ $N$ is suspended with the help of a string. The ball is pulled by a horizontal force $F$ such that the string makes an angle of $30^o$ with t...

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GATE2016-1-7
A point mass $M$ is released from rest and slides down a spherical bowl (of radius $R$) from a height $H$ as shown in the figure below. The surface of the bowl is smooth (no friction). The velocity of the mass at the bottom of the bowl is $\sqrt{gH}$ $\sqrt{2gR}$ $\sqrt{2gH}$ $0$

A point mass $M$ is released from rest and slides down a spherical bowl (of radius $R$) from a height $H$ as shown in the figure below. The surface of the bowl is smooth ...

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GATE2015-3-46
For the overhanging beam shown in figure, the magnitude of maximum bending moment (in $kN$-$m$) is ________

For the overhanging beam shown in figure, the magnitude of maximum bending moment (in $kN$-$m$) is ________

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GATE2015-3-48
A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________

A cantilever bracket is bolted to a column using three M$12×1.75$ bolts P, Q and R. The value of maximum shear stress developed in the bolt P (in $MPa$) is ________

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