Recent questions tagged gateme-2019-set2

The state of stress at a point in a component is represented by a Mohr’s circle of radius $100$ MPa centered at $200$ MPa on the thermal stress axis. On a plane passing t...

A wire of circular cross-section of diameter $1.0$ mm is bent into a circular arc of radius. $1.0$ m by application of pure bending moments at its ends. The Young’s modul...

Water enters a circular pipe of length $L=5.0$ m and diameter $D=0.20$m with Reynolds number $Re_D=500$. The velocity profile at the inlet of the pipe is uniform while it...

A thin vertical flat plate of height $L$, and infinite width perpendicular to the plane of the figure, is losing heat to the surroundings by natural convection. The tempe...

In an electrical discharge machining process, the breakdown voltage across inter electrode gap (IEG) is $200$ V and the capacitance of the RC circuit is $50 \mu F$. The e...

Given a vector $\overrightarrow{u} = \dfrac{1}{3} \big(-y^3 \hat{i} + x^3 \hat{j} + z^3 \hat{k} \big)$ and $\hat{n}$ as the unit normal vector to the surface of the hemi...

A diffferential equation is given as $$x^2 \frac{d^2y}{dx^2} – 2x \frac{dy}{dx} +2y =4$$ The solution of the differential equation in terms of arbitrary constants $C_1$ a...

The derivative of $f(x)= \cos x$ can be estimated using the approximation $f’(x)=\dfrac{f(x+h)-f(x-h)}{2h}$. The percentage error is calculated as $\bigg( \dfrac{\text{Ex...

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...

Consider two concentric circular cylinders of different materials $M$ and $N$ in contact with each other at $r=b$, as shown below. The interface at $r=b$ is frictionless....

A prismatic, straight, elastic, cantilever beam is subjected to a linearly distributed transverse load as shown below. If the beam length is $L$, Young’s modulus $E$, and...

A slender uniform rigid bar of mass $m$ is hinged at $O$ and supported by two springs, with stiffness, $3k$ and $k$ and a damper with damping coefficient $c$, as shown in...

The figure shows a heat engine (HE) working between two reservoirs. The amount of heat $(Q_2)$ rejected by the heat engine is drawn by a heat pump (HP). The heat pump rec...

The binary phase diagram of metals $P$ and $Q$ is shown in the figure. An alloy $X$ containing $60 \% P$ and $40 \% Q$ (by weight) is cooled from liquid to solid state. T...

The activities of a project, their duration and the precedence relationships are given in the table. For example, in a precedence relationship $”X<Y,Z”$ means that $X$ is...

The crank of a slider-crank mechanism rotates counter-clockwise (CCW) with a constant angular velocity $\omega$, as shown. Assume the length of the crank to be $r$.Using ...

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...

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...

The probability that a part manufactured by a company will be defective is $0.05$. If $15$ such parts are selected randomly and inspected, then the probability that at le...

A uniform disc with radius $r$ and a mass $m$ kg is mounted centrally on a horizontal axle of negligible mass and length of $1.5r$. The disc spins counter-clockwise about...

A short shoe external drum brake is shown in the figure. The diameter of the brake drum is $500 \: mm$. The dimensions $a=1000 \: mm, \: b=500 \: mm$ and $c=200 \: mm$. T...

Water flows through two different pipes $A$ and $B$ of the same circular cross-section but at different flow rates. The length of pipe $A$ is $1.0 \: m$ and that of pipe ...

The aerodynamic drag on a sports car depends on its shape. The car has a drag coefficient of $0.1$ with the windows and the roof closed. With the windows and the roof ope...

Three sets parallel plates $LM$, $NR$ and $PQ$ are given in Figures $1$, $2$ and $3$. The view factor $F_{IJ}$ is defined as the fraction of radiation leaving plate $I$ t...

Hot and cold fluids enter a parallel flow double tube heat exchanger at $100^{\circ}C$ and $15^{\circ} C$, respectively. The heat capacity rates of hot and cold fluids ar...

Water flowing at the rate of $1$ kg/s through a system is heated using an electric heater such that the specific enthalpy of the water increases by $2.50 \: kJ/kg$ and th...

An idealized centrifugal pump (blade outer radius of $50 \: mm$) consumes $2 \: kW$ power while running at $3000 \: rpm$. The entry of the liquid into the pump is axial a...

An air standard Otto cycle has thermal efficiency of $0.5$ and the mean effective pressure of the cycle is $1000 \: kPa$. For air, assume specific heat ratio $\gamma=1.4$...

The figure shows a pouring arrangement for casting of a metal block. Frictional losses are negligible. The acceleration due to gravity is $9.81 \: m/s^2$ .The time (in $s...