Questions by gatecse

Consider a vector $\text{p}$ in $2$-dimensional space. Let its direction (counter-clockwise angle with the positive $\text{x}$-axis) be $\theta$. Let $\text{p}$ be an ei...

Let $\text{C}$ represent the unit circle centered at origin in the complex plane, and complex variable, $z=x+iy$. The value of the contour integral $\oint _{C}\dfrac{\cos...

A set of jobs $\text{A, B, C, D, E, F, G, H}$ arrive at time $t= 0$ for processing on turning and grinding machines. Each job needs to be processed in sequence first on ...

The fundamental thermodynamic relation for a rubber band is given by $dU=TdS+\tau dL$, where $\text{T}$ is the absolute temperature, $\text{S}$ is the entropy, $\tau$ is ...

Consider a two degree of freedom system as shown in the figure, where $\text{PQ}$ is a rigid uniform rod of length, $\text{b}$ and mass, $\text{m}$.Assume that the spring...

​​​​​​A right solid circular cone standing on its base on a horizontal surface is of height $\text{H}$ and base radius $\text{R}$. The cone is made of a material with spe...

A tappet valve mechanism in an $\text{IC}$ engine comprises a rocker arm $\text{ABC}$ that is hinged at $\text{B}$ as shown in the figure. The rocker is assumed rigid and...

Customers arrive at a shop according to the Poisson distribution with a mean of $10$ customers/hour. The manager notes that no customer arrives tor the first $3$ minutes ...

A true centrifugal casting operation needs to be performed horizontally to make copper tube sections with outer diameter of $\text{250 mm}$ and inner diameter of $\text{2...

The resistance spot welding of two $\text{1.55 mm}$ thick metal sheets is performed using welding current of $\text{10000 A}$ for $\text{0.25 s}$. The contact resistance ...

An orthogonal cutting operation is performed using a single point cutting tool with a rake angle of $12^{\circ}$ on a lathe. During turning, the cutting force and the fri...

In a grinding operation of a metal, specific energy consumption is $15 \text{ J/mm}^{3}$. If a grinding wheel with a diameter of $\text{200 mm}$ is rotating at $\text{300...

A $\text{200 mm}$ wide plate having a thickness of $\text{20 mm}$ is fed through a rolling mill with two rolls. The radius of each roll is $\text{300 mm}$. The plate thic...

The $\text{XY}$ table of a $\text{NC}$ machine tool is to move from $P(1,1)$ to $Q(51,1)$; all coordinates are in $\text{mm}$. The pitch of the $\text{NC}$ drive leadscre...

Consider a single machine workstation to which jobs arrive according to a Poisson distribution with a mean arrival rate of $12$ jobs/hour. The process time of the worksta...

An uninsulated cylindrical wire of radius $\text{1.0 mm}$ produces electric heating at the rate of $\text{5.0 W/m}$. The temperature of the surface of the wire is $75\;^{...

A solid sphere of radius $\text{10 mm}$ is placed at the centroid of a hollow cubical enclosure of side length $\text{30 mm}$. The outer surface of the sphere is denoted ...

Consider a steam power plant operating on an ideal reheat Rankine cycle. The work input to the pump is $\text{20 kJ/kg}$. The work output from the high pressure turbine i...