State the torsion equation for a circular shaft and define the terms.

$\dfrac{T}{J} = \dfrac{\tau}{r} = \dfrac{G\theta}{L}$, where $T$ is torque, $J$ the polar moment of area, $\tau$ shear stress at radius $r$, $G$ the shear modulus, $\theta$ the angle of twist and $L$ the shaft length.

Give the polar moment of inertia $J$ for a solid and a hollow circular shaft.

Solid: $J = \dfrac{\pi d^{4}}{32}$. Hollow: $J = \dfrac{\pi (d_o^{4} - d_i^{4})}{32}$, where $d_o$ and $d_i$ are outer and inner diameters.

Where is shear stress maximum in a shaft under torsion, and what is the power-torque relation?

Shear stress is maximum at the outer surface (largest $r$). Power transmitted: $P = T\omega = \dfrac{2\pi N T}{60}$, with $N$ in rpm and $\omega$ in rad/s.

What is the torsional stiffness of a shaft?

$k_t = \dfrac{T}{\theta} = \dfrac{GJ}{L}$, the torque required per unit angle of twist.

Define beam deflection and write the governing Euler-Bernoulli differential equation.

Deflection is the transverse displacement $y$ of the beam axis. Governing equation: $EI\dfrac{d^{2}y}{dx^{2}} = M(x)$, where $EI$ is the flexural rigidity.

Give the maximum deflection for a simply supported beam with a central point load $W$.

$\delta_{max} = \dfrac{W L^{3}}{48 EI}$, occurring at mid-span.

Give the maximum deflection of a cantilever of length $L$ with an end point load $W$ and with a UDL $w$.

End load: $\delta_{max} = \dfrac{W L^{3}}{3EI}$. Uniformly distributed load: $\delta_{max} = \dfrac{w L^{4}}{8EI}$, both at the free end.

State the maximum principal stress (Rankine) theory of failure.

Failure occurs when the maximum principal stress reaches the uniaxial yield (or ultimate) strength: $\sigma_1 = \sigma_y$. Best suited to brittle materials.

State the maximum shear stress (Tresca / Guest) theory of failure.

Yielding begins when the maximum shear stress equals that at yield in a tensile test: $\dfrac{\sigma_1 - \sigma_3}{2} = \dfrac{\sigma_y}{2}$, i.e. $\sigma_1 - \sigma_3 = \sigma_y$. Suited to ductile materials.

State the distortion energy (von Mises) theory of failure.

Yielding occurs when the von Mises stress equals the yield stress: $\sqrt{\dfrac{(\sigma_1-\sigma_2)^{2}+(\sigma_2-\sigma_3)^{2}+(\sigma_3-\sigma_1)^{2}}{2}} = \sigma_y$. Most accurate for ductile metals.

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GATE Mechanical Engineering (ME) Flashcards

54 question-and-answer cards covering Mechanical Engineering (ME) as it is examined in GATE. 24 of them are printed below, taken from across the deck — no signup, no paywall on the preview.

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24 sample cards from the Mechanical Engineering (ME) deck

Sampled from the end of the deck, so these are different cards from the ones shown on the syllabus page.

State the torsion equation for a circular shaft and define the terms.
$\dfrac{T}{J} = \dfrac{\tau}{r} = \dfrac{G\theta}{L}$, where $T$ is torque, $J$ the polar moment of area, $\tau$ shear stress at radius $r$, $G$ the shear modulus, $\theta$ the angle of twist and $L$ the shaft length.
Give the polar moment of inertia $J$ for a solid and a hollow circular shaft.
Solid: $J = \dfrac{\pi d^{4}}{32}$. Hollow: $J = \dfrac{\pi (d_o^{4} - d_i^{4})}{32}$, where $d_o$ and $d_i$ are outer and inner diameters.
Where is shear stress maximum in a shaft under torsion, and what is the power-torque relation?
Shear stress is maximum at the outer surface (largest $r$). Power transmitted: $P = T\omega = \dfrac{2\pi N T}{60}$, with $N$ in rpm and $\omega$ in rad/s.
What is the torsional stiffness of a shaft?
$k_t = \dfrac{T}{\theta} = \dfrac{GJ}{L}$, the torque required per unit angle of twist.
Define beam deflection and write the governing Euler-Bernoulli differential equation.
Deflection is the transverse displacement $y$ of the beam axis. Governing equation: $EI\dfrac{d^{2}y}{dx^{2}} = M(x)$, where $EI$ is the flexural rigidity.
Give the maximum deflection for a simply supported beam with a central point load $W$.
$\delta_{max} = \dfrac{W L^{3}}{48 EI}$, occurring at mid-span.
Give the maximum deflection of a cantilever of length $L$ with an end point load $W$ and with a UDL $w$.
End load: $\delta_{max} = \dfrac{W L^{3}}{3EI}$. Uniformly distributed load: $\delta_{max} = \dfrac{w L^{4}}{8EI}$, both at the free end.
State the maximum principal stress (Rankine) theory of failure.
Failure occurs when the maximum principal stress reaches the uniaxial yield (or ultimate) strength: $\sigma_1 = \sigma_y$. Best suited to brittle materials.
State the maximum shear stress (Tresca / Guest) theory of failure.
Yielding begins when the maximum shear stress equals that at yield in a tensile test: $\dfrac{\sigma_1 - \sigma_3}{2} = \dfrac{\sigma_y}{2}$, i.e. $\sigma_1 - \sigma_3 = \sigma_y$. Suited to ductile materials.
State the distortion energy (von Mises) theory of failure.
Yielding occurs when the von Mises stress equals the yield stress: $\sqrt{\dfrac{(\sigma_1-\sigma_2)^{2}+(\sigma_2-\sigma_3)^{2}+(\sigma_3-\sigma_1)^{2}}{2}} = \sigma_y$. Most accurate for ductile metals.
State Euler's formula for the critical buckling load of a column.
$P_{cr} = \dfrac{\pi^{2} EI}{L_e^{2}}$, where $L_e$ is the effective length and $EI$ the flexural rigidity. Buckling occurs about the axis of least $I$.
Give the effective length $L_e$ for the four standard end conditions of a column.
Both ends pinned: $L_e = L$; both fixed: $L_e = 0.5L$; one fixed–one free: $L_e = 2L$; one fixed–one pinned: $L_e = 0.707L$.
Define slenderness ratio and the limitation of Euler's theory.
Slenderness ratio $= \dfrac{L_e}{k}$, where $k = \sqrt{I/A}$ is the radius of gyration. Euler's formula is valid only for long (slender) columns where the critical stress stays below the proportional limit; short columns fail by crushing.
Distinguish a mechanism, a machine and a kinematic chain.
A kinematic chain is an assembly of links connected by joints with relative motion possible. A mechanism is a kinematic chain with one link fixed. A machine is a mechanism (or set) that transmits forces to do useful work.
State Kutzbach's (Grübler's) equation for the degrees of freedom of a planar mechanism.
$F = 3(n-1) - 2j_1 - j_2$, where $n$ is the number of links, $j_1$ the number of lower (1-DOF) pairs and $j_2$ the number of higher (2-DOF) pairs.
State Grashof's law for a four-bar linkage.
For at least one link to make a full revolution, the sum of the shortest ($s$) and longest ($l$) links must be less than or equal to the sum of the other two ($p$, $q$): $s + l \leq p + q$.
Differentiate a lower pair from a higher pair, giving examples.
A lower pair has surface (area) contact between links (e.g. revolute/pin, prismatic/slider, screw). A higher pair has point or line contact (e.g. cam-follower, meshing gear teeth, ball bearing).
Define the base circle, pressure angle and pitch curve of a cam.
Base circle: smallest circle tangent to the cam profile (defines minimum radius). Pressure angle: angle between the direction of follower motion and the normal to the cam profile at the contact point. Pitch curve: locus of the trace point of the follower's reference.
State the law of gearing and define the module of a gear.
Law of gearing: the common normal to the tooth profiles at the point of contact must always pass through the fixed pitch point, giving a constant velocity ratio. Module $m = \dfrac{d}{T}$, the pitch-circle diameter $d$ per number of teeth $T$ (in mm).
For a pair of meshing gears, write the velocity (gear) ratio.
$\dfrac{N_1}{N_2} = \dfrac{T_2}{T_1} = \dfrac{d_2}{d_1}$, i.e. speed is inversely proportional to the number of teeth (and pitch diameter).
What is the function of a flywheel, and what is the coefficient of fluctuation of speed?
A flywheel stores and releases kinetic energy to smooth out speed fluctuations caused by varying torque, keeping speed nearly constant. Coefficient of fluctuation of speed $C_s = \dfrac{N_{max}-N_{min}}{N} = \dfrac{\omega_{max}-\omega_{min}}{\omega}$.
Relate the maximum fluctuation of energy of a flywheel to its mass moment of inertia.
$\Delta E = I\,\omega^{2}\,C_s = m k^{2}\,\omega^{2}\,C_s$, where $I$ is the mass moment of inertia, $\omega$ the mean angular speed and $C_s$ the coefficient of fluctuation of speed.
What is the function of a governor, and how does it differ from a flywheel?
A governor controls the mean speed over time by regulating fuel/working-fluid supply as the load varies (works between cycles). A flywheel limits speed fluctuation within a single cycle; it does not control the mean speed.
State the conditions for complete static and dynamic balancing of rotating masses.
Static (force) balance: $\sum m r = 0$ — the resultant of centrifugal forces is zero. Dynamic balance also requires $\sum m r l = 0$ — the resultant couple about any reference plane is zero. Both must hold for complete balance.

What this deck covers

The Mechanical Engineering (ME) deck follows the GATE Mechanical Engineering (ME) syllabus — 5 chapters and 19 topics — so questions land on material that is genuinely examinable rather than trivia around it. That works out to roughly 10.8 cards per chapter.

Answers are written to be recallable, not just readable — averaging about 180 characters, which is long enough to carry the reasoning and short enough to say out loud.

A deck like this earns its keep on the second and third pass. Read the syllabus first so you know the shape of the subject, then use the cards to find the specific facts that have not stuck.

Mechanical Engineering (ME) flashcards FAQ

How many Mechanical Engineering (ME) flashcards are in this GATE deck?

54 cards. This page previews 24 of them, sampled evenly across the deck so you can judge the difficulty before installing anything.

Are these GATE flashcards free?

Yes. The preview here is free to read with no signup, and the full 54-card deck is free inside the Examius app.

What do the Mechanical Engineering (ME) cards cover?

They follow the GATE Mechanical Engineering (ME) syllabus — 5 chapters and 19 topics — so the questions track what is actually examinable.

How should I use these flashcards?

Read the syllabus first so you know the shape of the subject, then drill the deck. Examius schedules each card with spaced repetition, so cards you keep missing come back sooner and ones you know drift further apart.