Most viewed questions in Applied Mechanics and Design / GO Mechanical

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GATE2018-2-33
A bimetallic cylindrical bar cross sectional area $1 \: m^2$ is made by bonding Steel (Young's modulus $= 210 \: GPa$) and Aluminium (Young's modulus =$70 \: GPa$) as shown in the figure. To maintain tensile axial strain of magnitude $10^{-6}$ in ... in Aluminium bar, the magnitude of the required force $P$ (in $kN$) along the indicated direction is $70$ $140$ $210$ $280$

A bimetallic cylindrical bar cross sectional area $1 \: m^2$ is made by bonding Steel (Young's modulus $= 210 \: GPa$) and Aluminium (Young's modulus =$70 \: GPa$) as sho...

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GATE2019 ME-2: 29
A ball of mass $3$ kg moving with a velocity of $4 \:m/s$ undergoes a perfectly-elastic direct-central impact with a stationary ball of mass $m$. After the impact is over, the kinetic energy of the $3$ kg ball is $6$ J. The possible value(s) of $m$ is/are $1$ kg only $6$ kg only $1$ kg, $6$ kg $1$ kg, $9$ kg

A ball of mass $3$ kg moving with a velocity of $4 \:m/s$ undergoes a perfectly-elastic direct-central impact with a stationary ball of mass $m$. After the impact is over...

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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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GATE2019 ME-2: 7
A spur gear has pitch circle diameter $D$ and number of teeth $T$. The circular pitch of the gear is $\dfrac{\pi D}{T} \\$ $\dfrac{T}{D} \\$ $\dfrac{D}{T} \\$ $\dfrac{2 \pi D}{T}$

A spur gear has pitch circle diameter $D$ and number of teeth $T$. The circular pitch of the gear is $\dfrac{\pi D}{T} \\$$\dfrac{T}{D} \\$$\dfrac{D}{T} \\$$\dfrac{2 \pi ...

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GATE2020-ME-1: 30
The truss shown in the figure has four members of length $\text{l}$ and flexural rigidity $\text{EI}$, and one member of length $l\sqrt{2}$ and flexural rigidity $\text{4EI}$. The truss is loaded by a pair of forces of magnitude $\text{P}$ ... $\dfrac{2\pi ^{2}EI}{l^{2}} \\$ $\dfrac{\pi ^{2}EI}{2l^{2}}$

The truss shown in the figure has four members of length $\text{l}$ and flexural rigidity $\text{EI}$, and one member of length $l\sqrt{2}$ and flexural rigidity $\text{4...

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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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GATE2020-ME-1: 5
The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load $P > 0$ with no appreciable deformation of the truss (i.e.with no appreciable change in angles between the members), are $BF$ and $DH$ only $BF, DH,$ and $GC$ only $BF, DH, GC, CD$ and $DE$ only $BF, DH, GC, FG$ and $GH$ only

The members carrying zero force (i.e. zero-force members) in the truss shown in the figure, for any load $P 0$ with no appreciable deformation of the truss (i.e.with no ...

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GATE2018-1-19
A steel column of rectangular section ($15$ mm $\times \: 10$ mm) and length $1.5$ m is simply supported at both ends. Assuming modulus of elasticity, $E=200$ GPa for steel, the critical axial load (in kN) is ______ (correct to two decimal places).

A steel column of rectangular section ($15$ mm $\times \: 10$ mm) and length $1.5$ m is simply supported at both ends. Assuming modulus of elasticity, $E=200$ GPa for ste...

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GATE2015-1-42
A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to center of gravity (CG) of the mobile and the rest of the dimensions of the mobile phone are shown. The mobile is kept on a ... RPM for which the mobile will get just lifted off the ground at the end $Q$ is approximately $3000$ $3500$ $4000$ $4500$

A mobile phone has a small motor with an eccentric mass used for vibrator mode. The location of the eccentric mass on motor with respect to center of gravity (CG) of the ...

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GATE2018-1-6
If $\sigma_1$ and $\sigma_3$ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is $\dfrac{\sigma_1 +\sigma_3}{2} \\$ $\dfrac{\sigma_1 -\sigma_3}{2} \\ $ $\sqrt{\dfrac{\sigma_1 +\sigma_3}{2}} \\$ $\sqrt{\dfrac{\sigma_1 -\sigma_3}{2}}$

If $\sigma_1$ and $\sigma_3$ are the algebraically largest and smallest principal stresses respectively, the value of the maximum shear stress is$\dfrac{\sigma_1 +\sigma_...

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GATE2017 ME-1: 42
A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3), S(0, 3)$ ... . The deformed length of the elongated diagonal, up to three decimal places is _______ units.

A rectangular region in a solid is in a state of plane strain. The $(x, y)$ coordinates of the corners of the undeformed rectangle are given by $P(0, 0), Q(4, 0), R(4, 3)...

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GATE2020-ME-1: 40
The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever. Taking the density of water as $1000\:kg/m^{3}$ , and the acceleration due to gravity as $10\:m/s^{2}$ , the maximum absolute bending moment developed in the cantilever is _________$kN\cdot m$ (round off to the nearest integer).

The barrier shown between two water tanks of unit width $(1\: m)$ into the plane of the screen in modeled as a cantilever.Taking the density of water as $1000\:kg/m^{3}$ ...

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GATE2015-2-36
A single-degree-freedom spring-mass system is subjected to a sinusoidal force of $10$ $N$ amplitude and frequency $ω$ along the axis of the spring. The stiffness of the spring is $150$ $N/m$, damping factor is $0.2$ and the undamped natural frequency is $10ω$. At steady state, the amplitude of vibration (in $m$) is approximately $0.05$ $0.07$ $0.70$ $0.90$

A single-degree-freedom spring-mass system is subjected to a sinusoidal force of $10$ $N$ amplitude and frequency $ω$ along the axis of the spring. The stiffness of the ...

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GATE2018-2-21
Fatigue life of a material for a fully reversed loading condition is estimated from $\sigma_a=1100N^{-0.15}$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ is the failure life in cycles. The maximum allowable stress amplitude (in $MPa$) for a life of $1 \times 10^5$ cycles under the same loading condition is ________ (correct to two decimal places).

Fatigue life of a material for a fully reversed loading condition is estimated from $$\sigma_a=1100N^{-0.15}$$, where $\sigma_a$ is teh stress amplitude in $MPa$ and $N$ ...

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GATE2018-1-41
A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45$^{\circ}$ and force of $40$ N is acting towards the left on the slider. The length of the crank is $30$ mm and the connecting rod is $70$ mm. ... inertial forces, the magnitude of the crankshaft torque (in Nm) needed to keep the mechanism in equilibrium is ______ (correct to two decimal places)

A slider crank mechanism is shown in the figure. At some instant, the crank angle is 45$^{\circ}$ and force of $40$ N is acting towards the left on the slider. The length...

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GATE2017 ME-1: 48
A $10$ mm deep cylindrical cup with diameter of $15$ mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto $2$ decimal points accuracy) of the blank is _________ mm.

A $10$ mm deep cylindrical cup with diameter of $15$ mm is drawn from a circular blank. Neglecting the variation in the sheet thickness, the diameter (upto $2$ decimal po...

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GATE2019 ME-1: 19
A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the block is $0.2$. A horizontal force of $10$ N is applied on the block as shown in the figure. The magnitude of force of friction (in N) on the block is _____

A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the bloc...

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GATE2019 ME-1: 40
Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The Young’s modulus $E=200 \: GPa$, and the coefficient of thermal expansion $\alpha = 3 \times 10^{-6} K^{-1}$. The minimum temperature rise required to cause Euler buckling of the beam is _______$K$.

Consider a prismatic straight beam of length $L=\pi \: m$, pinned at the two ends as shown in the figure. The beam has a square cross-section of side $p=6 \: mm$. The You...

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GATE ME 2012 | Question: 44
A force of $400$ N is applied to the brake drum of $0.5$ m diameter in a band-brake system as shown in the figure, where the wrapping angle is $180^{\circ}$. If the coefficient of friction between the drum and the band is $0.25$, the braking torque applied, in N.m is $100.6$ $54.4$ $22.1$ $15.7$

A force of $400$ N is applied to the brake drum of $0.5$ m diameter in a band-brake system as shown in the figure, where the wrapping angle is $180^{\circ}$. If the coeff...

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GATE Mechanical 2014 Set 1 | Question: 35
A block weighing $200 N$ is in contact with a level plane whose coefficients of static and kinetic friction are $0.4$ and $0.2$, respectively. The block is acted upon by a horizontal force (in newton) $P=10t$, where $t$ denotes the time in seconds. The velocity (in $m/s$) of the block attained after $10$ seconds is _______

A block weighing $200 N$ is in contact with a level plane whose coefficients of static and kinetic friction are $0.4$ and $0.2$, respectively. The block is acted upon by ...

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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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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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GATE2018-2-6
A frictionless gear train is shown in the figure. The leftmost $12$-teeth gear is given a torque of $100 \: N-m$. The output torque from the $60$-teeth gear on the right in $N-m$ is $5$ $20$ $500$ $2000$

A frictionless gear train is shown in the figure. The leftmost $12$-teeth gear is given a torque of $100 \: N-m$. The output torque from the $60$-teeth gear on the right ...

Arjun

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GATE2017 ME-1: 43
A machine element has an ultimate strength $(\sigma _{u})$ of $600 N/mm^{2}$, and endurance limit $(\sigma _{en})$ of $250 N/mm^{2}$. The fatigue curve for the element on a $\log-\log$ plot is shown below. If the element is to be designed for a finite life of $10000$ cycles, the maximum amplitude of a completely reversed operating stress is _________ $N/mm^{2}$.

A machine element has an ultimate strength $(\sigma _{u})$ of $600 N/mm^{2}$, and endurance limit $(\sigma _{en})$ of $250 N/mm^{2}$. The fatigue curve for the element on...

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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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GATE2017 ME-1: 39
An initially stress-free massless elastic beam of length $L$ and circular cross-section with diameter $d$ $(d << L)$ is held fixed between two walls as shown. The beam material has Young's modulus $E$ and coefficient of thermal expansion $a$. If the beam is ... , the temperature rise required to cause the beam to buckle is proportional to $d$ $d^{2}$ $d^{3}$ $d^{4}$

An initially stress-free massless elastic beam of length $L$ and circular cross-section with diameter $d$ $(d << L)$ is held fixed between two walls as shown. The beam ma...

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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 ME 2013 | Question: 43
A hinged gate of length $5$ $m$, inclined at $30^\circ$ with the horizontal and with water mass on its left, is shown in the figure below. Density of water is $1000$ $kg$/$m^3$. The minimum mass of the gate in $kg$ per unit width (perpendicular to the plane of paper), required to keep it closed is $5000$ $6600$ $7546$ $9623$

A hinged gate of length $5$ $m$, inclined at $30^\circ$ with the horizontal and with water mass on its left, is shown in the figure below. Density of water is $1000$ $kg$...

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GATE ME 2013 | Question: 33
A pin jointed uniform rigid rod of weight $W$ and length $L$ is supported horizontally by an external force $F$ as shown in the figure below. The force $F$ is suddenly removed. At the instant of force removal, the magnitude of vertical reaction developed at the support is $\text{zero}$ $W/4$ $W/2$ $W$

A pin jointed uniform rigid rod of weight $W$ and length $L$ is supported horizontally by an external force $F$ as shown in the figure below. The force $F$ is suddenly re...

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GATE2020-ME-1: 29
The $2$ kg block shown in the figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness $5\: N/m$. The cord hinged at $\text{O}$ is initially unstretched and always remains elastic. The block is given a velocity $v$ ... $0.4\: m$ is $0.83$ $1.07$ $1.36$ $1.50$

The $2$ kg block shown in the figure (top view) rests on a smooth horizontal surface and is attached to a massless elastic cord that has a stiffness $5\: N/m$. ...

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GATE ME 2012 | Question: 20
In the mechanism given below, if the angular velocity of the eccentric circular disc is $1$ rad/s, the angular velocity (rad/s) of the follower link for the instant shown in the figure is $0.05$ $0.1$ $5.0$ $10.0$

In the mechanism given below, if the angular velocity of the eccentric circular disc is $1$ rad/s, the angular velocity (rad/s) of the follower link for the instant shown...

Andrijana3306

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GATE ME 2012 | Question: 49
Two steel truss members, AC and BC, each having cross sectional area of $100 mm^2$, are subjected to a horizontal force F as shown in the figure. All the joints are hinged. The maximum force F in kN that can be applied at $C$ such that the axial stress in any of the truss members DOES NOT exceed $100$ MPa is $8.17$ $11.15$ $14.14$ $22.30$

Two steel truss members, AC and BC, each having cross sectional area of $100 mm^2$, are subjected to a horizontal force F as shown in the figure. All the joints are hinge...

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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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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...

Arjun

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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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GATE Mechanical 2014 Set 1 | Question: 38
A rigid uniform rod $AB$ of length $L$ and mass $m$ is hinged at $C$ such that $AC = L/3$, $CB = 2L/3$. Ends $A$ and $B$ are supported by springs of spring constant k. The natural frequency of the system is given by $\sqrt{\dfrac{k}{2m}} \\$ $\sqrt{\dfrac{k}{m}} \\$ $\sqrt{\dfrac{2k}{m} } \\$ $\sqrt{\dfrac{5k}{m}}$

A rigid uniform rod $AB$ of length $L$ and mass $m$ is hinged at $C$ such that $AC = L/3$, $CB = 2L/3$. Ends $A$ and $B$ are supported by springs of spring constant k. Th...

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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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GATE ME 2013 | Question: 22
If two nodes are observed at a frequency of $1800$ $rpm$ during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in $rpm$ is $200$ $450$ $600$ $900$

If two nodes are observed at a frequency of $1800$ $rpm$ during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in $rpm$...

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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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GATE ME 2013 | Question: 4
A rod of length $L$ having uniform cross-sectional area $A$ is subjected to a tensile force $P$ as shown in the figure below. If the Young's modulus of the material varies linearly from $E_1$ to $E_2$ along the length of the rod, the normal stress developed at the section-$SS$ ... $\dfrac{P(E_1-E_2)}{A(E_1+E_2)} \\$ $\dfrac{PE_2}{AE_1} \\$ $\dfrac{PE_1}{AE_2}$

A rod of length $L$ having uniform cross-sectional area $A$ is subjected to a tensile force $P$ as shown in the figure below. If the Young’s modulus of the material var...

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