List of top Questions asked in GATE Engineering Sciences

The state of stress at the critical location in a structure is \[ \sigma_{xx} = 420 \, MPa, \sigma_{yy} = 100 \, MPa, \sigma_{zz} = 0, \tau_{xy} = \tau_{yz} = \tau_{zx} = 0 \] The yield stress of the material in uniaxial tension is $400 \, MPa$. Select the correct statement among the following:

The figure shows a column of rectangular cross section $100 \, mm \times 80 \, mm$. It carries a load of $60 \, kN$ at a point $30 \, mm$ from the edge $PQ$. The values of stress component $\sigma_{zz}$ on surfaces $PQQ'P'$ and $SRR'S'$, at points far away from both ends of the column, are respectively:

Consider an electric pole with dimensions as shown in the figure. Let the end $R$ be subjected to a vertical force $F$. The flexural rigidity of both vertical and horizontal bars is $EI$. Neglect the axial deflection of the vertical bar, and all effects of self-weight. The vertical deflection at end $R$ is:

A uniform cantilever beam has flexural rigidity $EI$ and length $L$. It is subjected to a concentrated force $F$ and moment $M = 2FL$ at the free end as shown. The deflection $(\delta)$ at the free end is:

A steel ball of mass $m = 10 \, kg$ is suspended from the ceiling of a moving carriage by two inextensible strings making $60^\circ$ with the horizontal as shown. The carriage has an acceleration $a$ such that the tension in the string on the right is double the tension in the string on the left. Take $g = 10 \, m/s^2$. The acceleration $a$ (in $m/s^2$) is ............. (rounded off to one decimal place).

A block of mass $m = 10 \, kg$ is lying on an inclined plane $PQ$ at $30^\circ$. The mass is restrained from sliding down by a force $F$ applied up the plane. The coefficient of friction is $\mu = 0.3$. Take $g = 10 \, m/s^2$. The smallest force $F$ (in N) required to prevent the block from sliding down is ............ (rounded off to one decimal place).

A spherical rigid ball of mass $10 \, kg$ is moving with a speed of $2 \, m/s$ in the direction shown. The ball collides with a rigid frictionless wall and rebounds at an angle $\alpha$ with a speed $v$, as shown. The coefficient of restitution is $0.9$. The angle $\alpha$ (in degrees) is ........... (rounded off to one decimal place).

A thin-walled, closed cylindrical vessel of inside diameter $d$ and wall thickness $t$ contains a fluid under pressure $p$. The figure shows a part of the cylindrical vessel; end caps are not shown. Consider the small element with sides parallel and perpendicular to the axis of the cylinder. The stresses $\sigma_1$ and $\sigma_2$ are:

A spring–mass system is shown in the figure below. Take the acceleration due to gravity as $g = 9.81 \, m/s^2$. The static deflection due to weight and the time period of oscillations, respectively, are:

A rod is subjected to three forces as shown in the figure on the left. An equivalent force system with forces $F_1$, $F_2$ and moment $M$ is shown in the figure on the right. The value of $M$ (in N·m) is ................ (rounded off to one decimal place).

A simply supported beam of length 3 m is loaded as shown in the figure. The magnitude of the shear force (in kN) at the mid-point of the beam is ............ (rounded off to one decimal place).

For a plane stress problem, the principal stresses are 100 MPa and 50 MPa. The magnitude of maximum shear stress (in MPa) in the material is ............... (rounded off to one decimal place).

A solid uniform rigid disk of mass $m$ and radius $R$ rolls without slipping along a horizontal surface $PQ$. The speed of the center of the disk is $v$. The disk then strikes a hurdle of height $\tfrac{3R}{20}$ at point $S$. During the impact, there is no rebound or slip at $S$ and no impulse from the surface $PQ$. The magnitude of the velocity of the center of the disk immediately after the impact is:

A cylinder made of rubber (length $= L$ and diameter $= d$) is inserted in a rigid container as shown in the figure. The rubber cylinder fits snugly in the rigid container. There is no wall friction. The modulus of elasticity of the rubber is $E$ and its Poisson’s ratio is $\nu$. The cylinder is subjected to a small uniform pressure $p$ as shown in the figure. The resulting axial strain ($\varepsilon_{zz}$) is:

Two moles of a monoatomic ideal gas at 10 atm and 300 K is expanded isothermally and reversibly to a pressure of 2 atm. The absolute value of work done by the system is (in kJ) .......... (rounded off to two decimal places).

An electrochemical cell consists of pure Zn electrode (anode) and a hydrogen electrode (cathode) in a dilute Zn$^{+2}$ solution. The overall reaction is: \[ Zn(s) + 2H^+ \rightarrow H_2 + Zn^{+2} \] If the overall cell potential is +0.690 V, then the value of $\ln \left( \frac{[Zn^{+2}]}{[H^+]^2} \right)$ is ........... (rounded off to two decimal places). Given: Pressure of hydrogen gas = 1 atm; Temperature = 298 K; \[ \frac{RT}{F} = 0.0256 \, V \] Standard reduction potentials: \[ Zn^{+2} + 2e^- \rightarrow Zn (E^0 = -0.762 \, V) \] \[ 2H^+ + 2e^- \rightarrow H_2 (E^0 = 0 \, V) \]

In a Raman spectroscopy experiment done at 300 K, a Raman line is observed at $200 \, cm^{-1} \, (\sim 25 \, meV)$. The ratio of the intensity of the Stokes line to that of the Anti-Stokes line is ............ (rounded off to two decimal places). Given: Boltzmann constant, $k = 8.62 \times 10^{-5} \, eV K^{-1}$

A plane truss is simply supported at $P$ and $R$ as shown. A downward force $F$ is applied at hinge $Q$. The axial force developed in member $PS$ is:

A massless rigid rod $OP$ of length $L$ is hinged frictionlessly at $O$. A concentrated mass $m$ is attached to end $P$ of the rod. Initially, the rod $OP$ is horizontal. Then, it is released from rest. There is gravity as shown. The rod acquires an angular velocity as it swings. The clockwise angular velocity of the rod, when it first reaches the vertical position as shown, is:

Two equivalent descriptions of the state of stress at a point are shown in the figure. The normal stresses $\sigma_1$ and $\sigma_2$ as shown on the right must be, respectively,

The state of strain at a point in a machine component is given as \[ \varepsilon_{xx} = 2.5 \times 10^{-4}, \varepsilon_{yy} = 2.0 \times 10^{-4}, \varepsilon_{zz} = -1.5 \times 10^{-4}, \] \[ \varepsilon_{xy} = 2.5 \times 10^{-4}, \varepsilon_{yz} = -0.5 \times 10^{-4}, \varepsilon_{zx} = -1.0 \times 10^{-4}. \] The volumetric strain at this point is .............

TTT diagram of a eutectoid steel is shown below. Match the heat treatment cycle (in Column I) with its microstructure (in Column II).

Which of the following statement(s) is/are true for an optical microscope?

Among the 14 Bravais lattices, there is no base-centred cubic unit cell. Which of the following statement(s) is/are true?

Specific heat ($C_v$) of a material was found to depend on temperature as shown below. Which of the following statement(s) is/are true?