Recent questions tagged gateme-2019-set1

A solid cube of side $1$ m is kept at a room temperature of $32^{\circ} C$. The coefficient of linear thermal expansion of the cube material is $1 \times 10^{-5} / ^{\cir...

During a high cycle fatigue test, a metallic specimen is subjected to cyclic loading with a mean stress of $+140$ MPa, and a minimum stress of $-70$ MPa. The $R$-ratio (m...

Water flows through a pipe with a velocity given by $\overrightarrow{V}= \bigg( \dfrac{4}{t}+x+y \bigg) \hat{j} \: m/s$, where $\hat{j}$ is the unit vector in the $y$ dir...

Air of mass $1$ kg, initially at $300$ K and $10$ bar, is allowed to expand isothermally till it reaches a pressure of $1$ bar. Assuming air as an ideal gas with gas cons...

Consider the stress-strain curve for an ideal elastic-plastic strain hardening metal as shown in the figure. The metal was loaded in uniaxial tension starting from $O$. U...

The set of equations $$\begin{array}{l} x+y+z=1 \\ ax-ay+3z=5 \\ 5x-3y+az=6 \end{array}$$has infinite solutions, if $a=$$-3$$3$$4$$-4$

A harmonic function is analytic if it satisfies the Laplace equation. If $u(x,y)=2x^2-2y^2+4xy$ is a harmonic function, then its conjugate harmonic function $v(x,y)$ is$4...

The variable $x$ takes a value between $0$ and $10$ with uniform probability distribution. The variable $y$ takes a value between $0$ and $20$ with uniform probability di...

A car having weight $W$ is moving in the direction as shown in the figure. The center of gravity (CG) of the car is located at height $h$ from the ground, midway between ...

In a four bar planar mechanism shown in the figure, $AB= 5 \: cm, AD=4 \: cm $ and $DC=2 \: cm$. In the configuration shown, both AB and DC are perpendicular to AD. The b...

The rotor of a turbojet engine of an aircraft has a mass $180 \: kg$ and polar moment of inertia $10 \: kg \cdot m^2$ about the rotor axis. The rotor rotates at a constan...

The wall of a constant diameter pipe of length $1 \: m$ is heated uniformly with flux $q’’$ by wrapping a heater coil around it. The flow at the inlet to the pipe is hydr...

A gas is heated in a duct as it flows over a resistance heater. Consider a $101 \: kW$ electric heating system. The gas enters the heating section of the duct at $100 \: ...

A plane-strain compression (forging) of a block is shown in the figure. The strain in the $z$-direction is zero. The yield strength $(S_y)$ in uniaxial tension/compressio...

In orthogonal turning of a cylindrical tube of wall thickness $5 \: mm$, the axial and the tangential cutting forces were measured as $1259 \: N$ and $1601 \:N$, respecti...

A circular shaft having diameter $65.00_{-0.05}^{+0.01} \: mm$ is manufactured by turning process. A $50 \: \mu m$ thick coating of TiN is deposited on the shaft. Allowed...

Match the following sand mold casting defects with their respective causes.$\begin{array}{|l|l|l|l|} \hline \\ {} & \text{Defect} & {} & \text{Cause} \\ \hline P & \text{...

A truss is composed of members AB, BC, CD, AD and BD, as shown in the figure. A vertical load of $10 \: kN$ is applied at point D. The magnitude of force (in kN) in the m...

Consider an elastic straight beam of length $L= 10 \pi \: m$, with square cross-section of side $a=5 \: mm$, and Young’s modulus $E=200 \: GPa$. This straight beam was be...

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...

In a UTM experiment, a sample of length $100 \: mm$, was loaded in tension until failure. The failure load was $40 \: kN$. The displacement, measured using the cross-head...

At a critical point in a component, the state of stress is given as $\sigma_{xx}=100 \: MPa, \: \sigma_{yy}=220 \: MPa, \: \sigma_{xy}= \sigma_{yx} = 80 \: MPa$ and all o...

A uniform thin disk of mass $1 \: kg$ and radius $0.1 \: m$ is kept on a surface as shown in the figure. A spring of stiffness $k_1=400 \: N/m$ is connected to the disk c...

A single block brake with a short shoe and torque capacity of $250 \: N \cdot m$ is shown. The cylindrical brake drum rotates anticlockwise at $100 \: rpm$ and the coeffi...

Two immiscible, incompressible, viscous fluids having same densities but different viscosities are contained between two infinite horizontal parallel plates, $2 \: m$ apa...

A cube of side $100 \: mm$ is placed at the bottom of an empty container on one of its faces. The density of the material of the cube is $800 \: kg/m^3$. Liquid of densit...

Three slabs are joined together as shown in the figure. There is no thermal contact resistance at the interfaces. The center slab experiences a non-uniform internal heat ...

If one mole of $H_2$ has occupies a rigid container with a capacity of $1000$ litres and the temperature is raised from $27^{\circ} C$ to $37^{\circ} C$, the change in pr...

A gas turbine with air as the working fluid has an isentropic efficiency of $0.70$ when operating at a pressure ratio of $3$. Now, the pressure ratio of the turbine is in...