Recent questions tagged gateme-2019-set2 / GO Mechanical

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GATE2019 ME-2: 31
A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is $L$, Young’s modulus $E$, and area moment of inertia $I$, the magnitude of the maximum deflection is $\dfrac{qL^4}{15EI} \\$ $\dfrac{qL^4}{30EI} \\$ $\dfrac{qL^4}{10EI} \\$ $\dfrac{qL^4}{60EI}$

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is $L$, Young’s modulus $E$, a...

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GATE2019 ME-2: 32
A slender uniform rigid bar of mass $m$ is hinged at $O$ and supported by two springs, with stiffness, $3k$ and $k$ and a damper with damping coefficient $c$, as shown in the figure. For the system to be critically damped, the ratio $c/\sqrt{km}$ should be $2$ $4$ $2 \sqrt{7}$ $4 \sqrt{7}$

A slender uniform rigid bar of mass $m$ is hinged at $O$ and supported by two springs, with stiffness, $3k$ and $k$ and a damper with damping coefficient $c$, as shown in...

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GATE2019 ME-2: 33
The figure shows a heat engine (HE) working between two reservoirs. The amount of heat $(Q_2)$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump receives the entire work output $(W)$ of the heat engine. If temperatures, $T_1 >T_3>T_2$, then the relation between ... $\text{COP}= 1 + \eta$ $\text{COP}= \eta^{-1}$ $\text{COP}= \eta^{-1} -1 $

The figure shows a heat engine (HE) working between two reservoirs. The amount of heat $(Q_2)$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump rec...

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GATE2019 ME-2: 34
The binary phase diagram of metals $P$ and $Q$ is shown in the figure. An alloy $X$ containing $60 \% P$ and $40 \% Q$ (by weight) is cooled from liquid to solid state. The fractions of solid and liquid (in weight percent) at $1250^o C$, respectively, will be $77.8 \% \text{ and } 22.2 \%$ $22.2 \% \text{ and } 77.8 \%$ $68.0 \% \text{ and } 38.0 \%$ $32.0 \% \text{ and } 68.0 \%$

The binary phase diagram of metals $P$ and $Q$ is shown in the figure. An alloy $X$ containing $60 \% P$ and $40 \% Q$ (by weight) is cooled from liquid to solid state. T...

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GATE2019 ME-2: 35
The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship $ X<Y,Z $ means that $X$ is predecessor of activities $Y$ and $Z$ ... $17$ $21$ $23$ $25$

The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship $”X<Y,Z”$ means that $X...

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GATE2019 ME-2: 36
The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity $\omega$, as shown. Assume the length of the crank to be $r$. Using exact analysis, the acceleration of the slider in the $y$-direction, at the instant shown, where the crank is parallel to $x$-axis, is given by $- \omega ^2r$ $2 \omega ^2r$ $\omega ^2r$ $-2 \omega ^2r$

The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity $\omega$, as shown. Assume the length of the crank to be $r$.Using ...

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GATE2019 ME-2: 37
A horizontal cantilever beam of circular cross-section, length $1.0$ m and flexural rigidity $EI=200 \: N \cdot m^2$ is subjected to an applied moment $M_A = 1.0 \: N \cdot m$ at the free end as shown in the figure. The magnitude of the vertical deflection of the free end is ______ mm (round off to one decimal place).

A horizontal cantilever beam of circular cross-section, length $1.0$ m and flexural rigidity $EI=200 \: N \cdot m^2$ is subjected to an applied moment $M_A = 1.0 \: N \cd...

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GATE2019 ME-2: 38
Two masses $A$ and $B$ having mass $m_a$ and $m_b$, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis through O perpendicular to the plane of the figure. The radii of rotation of the masses $m_a$ ... $200$ mm is _________ kg (round off to two decimal places).

Two masses $A$ and $B$ having mass $m_a$ and $m_b$, respectively, lying in the plane of the figure shown, are rigidly attached to a shaft which revolves about an axis thr...

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GATE2019 ME-2: 39
A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link $2$ is rotating anticlockwise with a constant angular speed $\omega_2$. Length of different links are: $O_2 O_4=O_2A=L,$$AB=O_4B=\sqrt{2}L$ The magnitude of ... $O_2O_4$ as shown. The ratio $\frac{\omega_4}{\omega_2}$ is _________ (round off to two decimal places).

A four bar mechanism is shown in the figure. The link numbers are mentioned near the links. Input link $2$ is rotating anticlockwise with a constant angular speed $\omega...

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GATE2019 ME-2: 40
The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at least two parts will be defective is _____ (round off to two decimal places).

The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at le...

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GATE2019 ME-2: 41
A uniform disc with radius $r$ and a mass $m$ kg is mounted centrally on a horizontal axle of negligible mass and length of $1.5r$. The disc spins counter-clockwise about the axle with angular speed $\omega$, when viewed from the right-hand side bearing, ... $g=10 m/s^2$, the ratio of the larger to the smaller bearing reaction force (considering appropriate signs) is ______

A uniform disc with radius $r$ and a mass $m$ kg is mounted centrally on a horizontal axle of negligible mass and length of $1.5r$. The disc spins counter-clockwise about...

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GATE2019 ME-2: 42
A short shoe external drum brake is shown in the figure. The diameter of the brake drum is $500 \: mm$. The dimensions $a=1000 \: mm, \: b=500 \: mm$ and $c=200 \: mm$. The coefficient of friction between the drum and the shoe is $0.35$. ... in the figure. The drum is rotating anti-clockwise. The braking torque on the drum is ______ $N \cdot m$ (round off to two decimal places).

A short shoe external drum brake is shown in the figure. The diameter of the brake drum is $500 \: mm$. The dimensions $a=1000 \: mm, \: b=500 \: mm$ and $c=200 \: mm$. T...

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GATE2019 ME-2: 43
Water flows through two different pipes $A$ and $B$ of the same circular cross-section but at different flow rates. The length of pipe $A$ is $1.0 \: m$ and that of pipe $B$ is $2.0 \: m$. The flow in both the pipes is laminar and fully ... head loss across the length of the pipes is same, the ratio of volume flow rates $Q_B/Q_A$ is __________ (round off to two decimal places).

Water flows through two different pipes $A$ and $B$ of the same circular cross-section but at different flow rates. The length of pipe $A$ is $1.0 \: m$ and that of pipe ...

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GATE2019 ME-2: 44
The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of $0.1$ with the windows and the roof closed. With the windows and the roof open, the drag coefficient becomes $0.8$. The car travels at $44$ km/h with the ... round off to two decimal places), is __________ $km/h$ (The density of air and the frontal area may be assumed to be constant).

The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of $0.1$ with the windows and the roof closed. With the windows and the roof ope...

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GATE2019 ME-2: 45
Three sets parallel plates $LM$, $NR$ and $PQ$ are given in Figures $1$, $2$ and $3$. The view factor $F_{IJ}$ is defined as the fraction of radiation leaving plate $I$ that is intercepted by plate $J$. Assume that the values of $F_{LM}$ and $F_{NR}$ are $0.8$ and $0.4$, respectively. The value of $F_{PQ}$ (round off to one decimal place) is ____________

Three sets parallel plates $LM$, $NR$ and $PQ$ are given in Figures $1$, $2$ and $3$. The view factor $F_{IJ}$ is defined as the fraction of radiation leaving plate $I$ t...

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GATE2019 ME-2: 46
Hot and cold fluids enter a parallel flow double tube heat exchanger at $100^{\circ}C$ and $15^{\circ} C$, respectively. The heat capacity rates of hot and cold fluids are $C_h=2000 \: W/K$ and $C_c =1200 \: W/K$, respectively. If the outlet ... $45^{\circ} C$, the log mean temperature difference (LMTD) of the heat exchanger is __________ $K$ (round off to two decimal places).

Hot and cold fluids enter a parallel flow double tube heat exchanger at $100^{\circ}C$ and $15^{\circ} C$, respectively. The heat capacity rates of hot and cold fluids ar...

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GATE2019 ME-2: 47
Water flowing at the rate of $1$ kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by $2.50 \: kJ/kg$ and the specific entropy increases by $0.007 \: kJ/kg \cdot K$. The power input ... an ambient temperature of $300 \: K$, the irreversibility rate of the system is __________ $kW$ (round off to two decimal places).

Water flowing at the rate of $1$ kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by $2.50 \: kJ/kg$ and th...

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GATE2019 ME-2: 48
An idealized centrifugal pump (blade outer radius of $50 \: mm$) consumes $2 \: kW$ power while running at $3000 \: rpm$. The entry of the liquid into the pump is axial and exit from the pump is radial with respect to impeller. If the losses are neglected, then the mass flow rate of the liquid through the pump is ___________ $kg/s$ (round off to two decimal places)

An idealized centrifugal pump (blade outer radius of $50 \: mm$) consumes $2 \: kW$ power while running at $3000 \: rpm$. The entry of the liquid into the pump is axial a...

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GATE2019 ME-2: 49
An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$ and specific gas constant $R=0.287 \: kJ/kg \cdot K$. If the pressure and ... $300 \: K$, respectively, then the specific net work output of the cycle is _____ $kJ/kg $ (round off to two decimal places).

An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$...

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GATE2019 ME-2: 50
The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is $9.81 \: m/s^2$ .The time (in $s$, round off to two decimal places) to fill up the mold cavity (of size $40 \: cm \times 30 \: cm \times 15 \: cm$) is _____

The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is $9.81 \: m/s^2$ .The time (in $s...

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GATE2019 ME-2: 51
A gas tungsten arc welding operation is performed using a current of $250 \: A$ and an arc voltage of $20 \: V$ at a welding speed of $5 \: mm/s$. Assuming that the arc efficiency is $70 \%$, the net heat input per unit length of the weld will be _________$kJ/mm$ (round off to one decimal place)

A gas tungsten arc welding operation is performed using a current of $250 \: A$ and an arc voltage of $20 \: V$ at a welding speed of $5 \: mm/s$. Assuming that the arc e...

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GATE2019 ME-2: 52
The thickness of a sheet is reduced by rolling (without any change in width) using $600 \: mm$ diameter rolls. Neglect elastic deflection of the rolls and assume that the coefficient of friction at the roll-workpiece interface is $0.05$. The sheet enters ... final thickness that can be produced by this process in a single pass is __________ $mm$ (round off to two decimal places).

The thickness of a sheet is reduced by rolling (without any change in width) using $600 \: mm$ diameter rolls. Neglect elastic deflection of the rolls and assume that the...

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GATE2019 ME-2: 53
A through hole is drilled in an aluminium alloy plate of $15 \: mm$ thickness with a drill bit of diameter $10$ mm, at a feed of $0.25$ mm/rev and a spindle speed of $1200$ rpm. If the specific energy required for cutting this material is $0.7 \: N \cdot m/mm^3$, the power required for drilling is ____________$W$ (round off to two decimal places)

A through hole is drilled in an aluminium alloy plate of $15 \: mm$ thickness with a drill bit of diameter $10$ mm, at a feed of $0.25$ mm/rev and a spindle speed of $120...

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GATE2019 ME-2: 54
In an orthogonal machining with a single point cutting tool of rake angle $10^{\circ}$, the uncut chip thickness and the chip thickness are $0.125$ mm and $0.22$ mm, respectively. Using Merchant’s first solution for the condition of minimum cutting force, the coefficient of friction at the chip-tool interface is _______ (round off to two decimal places).

In an orthogonal machining with a single point cutting tool of rake angle $10^{\circ}$, the uncut chip thickness and the chip thickness are $0.125$ mm and $0.22$ mm, resp...

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GATE2019 ME-2: 55
The annual demand of valves per year in a company is $10,000$ units. The current order quantity is $400$ valves per order. The holding cost is Rs. $24$ per valve per year and the ordering cost is Rs. $400$ per order. If the current order ... Economic Order Quantity, then the saving in the total cost of inventory per year will be Rs. __________ (round off to two decimal places).

The annual demand of valves per year in a company is $10,000$ units. The current order quantity is $400$ valves per order. The holding cost is Rs. $24$ per valve per year...

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