Recent questions tagged gateme-2022-set1

The plane of the figure represents a horizontal plane. A thin rigid rod at rest is pivoted without friction about a fixed vertical axis passing through $O$. Its mass mome...

A rigid uniform annular disc is pivoted on a knife edge $A$ in a uniform gravitational field as shown, such that it can execute small amplitude simple harmonic motion in ...

Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and alumi...

A polytropic process is carried out from an initial pressure of $110$ $\text{kPa}$ and volume of $5\; m^{3}$ to a final volume of $2.5\; m^{3}$. The polytropic index is g...

The value of the integral $$\oint \left ( \frac{6z}{2z^{4} - 3z^{3} + 7z^{2} - 3z + 5 } \right )dz$$ evaluated over a counter-clockwise circular contour in the complex pl...

An $L$-shaped elastic member $\text{ABC}$ with slender arms $\text{AB}$ and $\text{BC}$ of uniform cross-section is clamped at end $A$ and connected to a pin at end $C$. ...

A planar four-bar linkage mechanism with $3$ revolute kinematic pairs and $1$ prismatic kinematic pair is shown in the figure, where $AB \perp CE$ and $FD \perp CE$. The ...

Consider a forced single degree-of-freedom system governed by $\ddot{\chi }\left ( t \right ) + 2 \zeta \omega _{n}\dot{\chi }\left ( t \right ) +\omega _{n}^{2}\chi(t)= ...

A bracket is attached to a vertical column by means of two identical rivets $U$ and $V$ separated by a distance of $2a = 100\; mm$, as shown in the figure. The permissibl...

In $Fe-Fe_{3}C$ phase diagram, the eutectoid composition is $0.8$ weight $\%$ of carbon at $725^{\circ}C$. The maximum solubility of carbon in $\alpha$-ferrite phase is $...

Activities $A$ to $K$ are required to complete a project. The time estimates and the immediate predecessors of these activities are given in the table. If the project is ...

A solid spherical bead of lead (uniform density= $11000 \; kg/m^{3}$) of diameter $d = 0.1\; mm$ sinks with a constant velocity $V$ in a large stagnant pool of a liquid (...

Consider steady, one-dimensional compressible flow or a gas in a pipe or diameter $1\; m$. At one location in the pipe, the density and velocity are $1\; kg/m^{3}$ and $1...

Consider a rod of uniform thermal conductivity whose one end $(x = 0)$ is insulated and the other end $(x =L)$ is exposed to flow of air at temperature $T_{\infty}$ with ...

The system of linear equations in real $\left ( x,y \right )$ given by $$\left ( x \: y \right )\begin{bmatrix} 2 &5 - 2 \alpha \\ \alpha & 1 \end{bmatrix} = \left ( 0\:0...

Let a random variable $X$ follow Poisson distribution such that $$\text{Prob (X = 1) = Prob (X = 2)}$$. The value of $\text{Prob (X = 3)}$ is ______________ (round off t...

Consider two vectors: $$\vec{a} = 5 i + 7j + 2k$$$$\vec{b} = 3 i - j + 6k$$Magnitude of the component of $\vec{a}$ orthogonal to $\vec{b}$ in the plane containing the vec...

A structure, along with the loads applied on it, is shown in the figure. Self-weight of all the members is negligible and all the pin joints are friction-less. $AE$ is a ...

Two rigid massless rods $PR$ and $RQ$ are joined at frictionless pin-joint $R$ and are resting on ground at $P$ and $Q$, respectively, as shown in the figure. A vertical ...

A cylindrical disc of $\text{mass m = 1 kg}$ and $\text{radius r = 0.15 m}$ was spinning at $\omega =5\; rad/s$ when it was placed on a flat horizontal surface and releas...

A thin-walled cylindrical pressure vessel has mean wall thickness of $t$ and nominal radius of $r$. The Poisson's ratio of the wall material is $1/3$. When it was subject...

A schematic of an epicyclic gear train is shown in the figure. The sun $\text{(gear 1)}$ and planet $\text{(gear 2)}$ are external, and the ring gear $\text{(gear 3)}$ is...

Under orthogonal cutting condition, a turning operation is carried out on a metallic workpiece at a cutting speed of $4\; m/s$. The orthogonal rake angle of the cutting t...

A $1$ $\text{mm}$ thick cylindrical tube, $100$ $\text{mm}$ in diameter, is orthogonally turned such that the entire wall thickness of the tube is cut in a single pass. T...

A $4$ $\text{mm}$ thick aluminum sheet of width $w = 100$ $\text{mm}$ is rolled in a two-roll mill of roll diameter $200$ $\text{mm}$ each. The workpiece is lubricated wi...

Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding process using the following welding parameters.$$\begin{ar...

An assignment problem is solved to minimize the total processing time of four jobs ($1,2,3$ and $4$) on four different machines such that each job is processed exactly by...

The product structure diagram shows the number of different components required at each level to produce one unit of the final product $P$. If there are $50$ units of on-...

Consider a one-dimensional steady heat conduction process through a solid slab of thickness $0.1\: m$. The higher temperature side $A$ has a surface temperature of $80^{\...