A rope with two mass-less platforms at its two ends passes over a fixed pulley as shown in the figure. Discs with narrow slots and having equal weight of $20\: N$ each can be placed on the platforms. The number of discs placed on the left side platform ... refer to part $\text{(ii)}$ of the figure) required to prevent downward motion of the left side platform is _____________________(in integer).
For a dynamical system governed by the equation. $\ddot{x}\left ( t \right ) + 2\zeta \omega _{n}\dot{x}\left ( t \right )+\omega _{n}^{2}x\left ( t \right ) = 0$ the damping ratio $\zeta$ ... . Neglecting higher powers $(>1)$ of the damping ratio, the displacement at the next peak in the positive direction will be __________________ $\text{mm}$ (in integer).
An electric car manufacturer underestimated the January sales of car by $20$ units, while the actual sales was $120$ units. If the manufacturer uses exponential smoothing method with a smoothing constant of $\alpha = 0.2$, then the sales forecast for the month of February of the same year is ____________ units (in integer).
The demand of a certain part is $1000$ parts/year and its cost is ₹$1000$/part. The orders are placed based on the economic order quantity $\text{(EOQ)}$. The cost of ordering is ₹$100$/order and the lead time for receiving the orders is $5$ days. If the holding cost is ₹$20$/part/year, the inventory level for placing the orders is ________________ parts (round off to the nearest integer).
Consider $1$ $\text{kg}$ of an ideal gas at $1$ bar and $300$ $K$ contained in a rigid and perfectly insulated container. The specific heat of the gas at constant volume $c_{v}$ is equal to $750 \:J \cdot kg^{-1}\cdot K^{-1}$. A ... work on the gas. Assume that the container does not participate in the thermodynamic interaction. The final pressure of the gas will be _____________ bar (in integer).
Wien's law is stated as follows: $\lambda _{m}T = C$, where $C$ is $2898$ $\mu m \cdot K$ and $\lambda_{m}$ is the wavelength at which the emissive power of a black body is maximum for a given temperature $T$. The spectral hemispherical ... $K$ (round off to the nearest integer).
If the sum and product of eigenvalues of a $2 \times 2$ real matrix $\begin{bmatrix} 3 & p\\ p & q \end{bmatrix}$ are $4$ and $-1$ respectively, then $\left | p \right |$ is ______________ (in integer).
Given $z = x + iy, i = \sqrt{-1}$. $C$ is a circle of radius $2$ with the centre at the origin. If the contour $C$ is traversed anticlockwise, then the value of the integral $\dfrac{1}{2\pi}\int _{C}\dfrac{1}{\left ( z-i \right )\left ( z+4i \right )}dz$ is __________________ (round off to one decimal place).
A shaft of length $L$ is made of two materials, one in the inner core and the other in the outer rim, and the two are perfectly joined together (no slip at the interface) along the entire length of the shaft. The diameter of the inner core is $d_{i}$ and the ... range and stress-strain relations are linear. Then the ratio $\tau_{i}/ \tau_{o}$ is ______________ (round off to $2$ decimal places).
A rigid beam $\text{AD}$ of length $3a = 6\:m$ is hinged at frictionless pin joint $A$ and supported by two strings as shown in the figure. String $\text{BC}$ passes over two small frictionless pulleys of negligible radius. All the strings are made of the ... . Assuming small deflections, the tension developed in the string at $C$ is _______________ $\text{kN}$ (round off to $2$ decimal places).
In the configuration of the planar four-bar mechanism at a certain instant as shown in the figure, the angular velocity of the $2$ $\text{cm}$ long link is $w_{2} = 5$ $\text{rad/s}$. Given the dimensions as shown, the magnitude of the angular velocity $w_{4}$ of the $4$ $\text{cm}$ long link is given by ______________ $\text{rad/s}$ (round off to $2$ decimal places).
A shaft $\text{AC}$ rotating at a constant speed carries a thin pulley of radius $r= 0.4\:m$ at the end $C$ which drives a belt. A motor is coupled at the end $A$ of the shaft such that it applies a torque $M_{z}$ about the shaft axis ... and fatigue loading and assuming maximum shear stress theory, the minimum required shaft diameter is _____________ $\text{mm}$ (round off to $2$ decimal places).
A straight-teeth horizontal slab milling cutter is shown in the figure. It has $4$ teeth and diameter $(D)$ of $200$ $\text{mm}$. The rotational speed of the cutter is $100$ $\text{rpm}$ and the linear feed given to the workpiece is $1000$ $\text{mm}$/minute. The ... of $\frac{d}{D}< < 1$ is invalid. The maximum cutting force required is _____________ $\text{kN}$ (round off to one decimal place).
ln an orthogonal machining operation, the cutting and thrust forces are equal in magnitude. The uncut chip thickness is $0.5$ $\text{mm}$ and the shear angle is $15^{\circ}$. The orthogonal rake angle of the tool is $0^{\circ}$ and the width of cut is $2$ ... and its yield shear strength is $500$ $\text{MPa}$. The cutting force is ___________________ $\text{N}$ (round off to the nearest integer).
The best size wire is fitted in a groove of a metric screw such that the wire touches the flanks of the thread on the pitch line as shown in the figure. The pitch $(p)$ and included angle of the thread are $4$ $\text{mm}$ and $60^{\circ}$, respectively. The diameter of the best size wire is _______________ $\text{mm}$ (round off to $2$ decimal places).
In a direct current arc welding process, the power source has an open circuit voltage of $100\: V$ and short circuit current of $1000 \:A$. Assume a linear relationship between voltage and current. The arc voltage $(V)$ varies with the arc length $(l)$ ... volts and $l$ is in $\text{mm}$. The maximum available arc power during the process is ________________ $\text{kVA}$ (in integer).
A cylindrical billet of $100$ $\text{mm}$ diameter and $100$ $\text{mm}$ length is extruded by a direct extrusion process to produce a bar of $L$-section. The cross sectional dimensions of this $L$-section bar are shown in the figure. The total extrusion pressure ... $1.05$, then the maximum force required at the start of extrusion is ________________ $\text{kN}$ (round off to one decimal place).
A project consists of five activities $\text{(A, B, C, D and E)}$. The duration of each activity follows beta distribution. The three time estimates (in weeks) of each activity and immediate predecessor$(s)$ are listed in the table. The expected time of the project completion is ________________ weeks (in integer ... time Pessimistic time A 4 5 6 None B 1 3 5 A C 1 2 3 A D 2 4 6 C E 3 4 5 B, D
A rigid tank of volume of $8 \:m^{3}$ is being filled up with air from a pipeline connected through a valve. Initially the valve is closed and the tank is assumed to be completely evacuated. The air pressure and temperature inside the pipeline are maintained ... The final temperature of the tank after the completion of the filling process is _______________ $K$ (round off to the nearest integer).
At steady state, $500$ $\text{kg/s}$ of steam enters a turbine with specific enthalpy equal to $3500$ $\text{kJ/kg}$ and specific entropy equal to $6.5$ ${kJ \cdot kg^{-1} \cdot K^{-1}}$. It expands reversibly in the turbine to the condenser pressure. Heat loss occurs ... ${kJ \cdot kg^{-1} \cdot K^{-1}}$, respectively, the work output from the turbine is ______________ $\text{MW}$ (in integer).
A uniform wooden rod (specific gravity = $0.6$, diameter = $4$ $\text{cm}$ and length = $8\:m$) is immersed in the water and is hinged without friction at point $A$ on the waterline as shown in the figure. A solid spherical ball made of lead (specific gravity = $11.4$) is ... $\pi = 3.14$. Radius of the ball is _____________ $\text{cm}$ (round off to $2$ decimal places).
Consider steady state, one-dimensional heat conduction in an infinite slab of thickness $2L (L = 1\:m)$ as shown in the figure. The conductivity $(k)$ of the material varies with temperature as $\text{k = CT}$, where $T$ is the temperature in $K$, and $C$ is a ... slab. If both faces of the slab are maintained at $600\: K$, then the temperature at $X = 0$ is _______________ $K$ (in integer).
Saturated vapor at $200\: ^{\circ}C$ condenses to saturated liquid at the rate of $150$ $\text{kg/s}$ on the shell side of a heat exchanger (enthalpy of condensation $h_{fg} = 2400$ $\text{kJ/kg}$ ... effectiveness of the heat exchanger is $0.9$, then the mass flow rate of the fluid in the tube side is ____________ $\text{kg/s}$ (in integer).
Consider a hydrodynamically and thermally fully-developed, steady fluid flow of $1$ $\text{kg/s}$ in a uniformly heated pipe with diameter of $0.1\: m$ and length of $40 \:m$. A constant heat flux of magnitude $15000\: W/m^{2}$ is imposed on the outer ... on the basis of the pipe diameter. The pipe surface temperature at the exit is _______________ $^{\circ}C$ (round off to the nearest integer).
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 moment of inertia is equal to $0.1\; kg.cm^{2}$ about $O$. A point mass of $0.001$ ... location shown, and sticks to it. Immediately after the impact, the angular velocity of the rod is ______________ $\text{rad/s}$ (in integer).
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 the plane of the figure without slip at the pivot point. The inner radius $r$ ... $\beta =$ ____________________ (round off to $2$ decimal places).
Electrochemical machining operations are performed with tungsten as the tool, and copper and aluminum as two different workpiece materials. Properties of copper and aluminum are given in the table below. ... $\text{MRR}$ of aluminum will be _______________________ $\text{mg/s}$ (round-off to two decimal places)
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 given by $n = 1.2$. The absolute value of the work done during the process is ______________ $\text{kJ}$ (round off to $2$ decimal places).
A flat plate made of cast iron is exposed to a solar flux of $600\; W/m^{2}$ at an ambient temperature of $25^{\circ}C$ ... radiation. Under the aforementioned conditions, the radiation equilibrium temperature of the plate is _____________$^{\circ}C$ (round off to the nearest integer).
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 to $2$ decimal places).
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 vectors $\vec{a}$ and $\vec{b}$ is _____________ (round off to $2$ decimal places).
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 single member that contains pin $C$. Likewise, $BE$ ... $GI$ and $FH$ are overlapping rigid members. The magnitude of the force carried by member $CI$ is ______________ $kN$ (in integer).
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 force $F$ acts on the pin $R$ as shown. When the included angle $\theta < 90^{\circ}$, ... of the coefficient of friction at $Q$ to that at $P\left(\mu_{Q}/\mu_{P}\right)$ is ___________________ (round off to two decimal places).
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 released (refer to the figure). Gravity $g$ acts vertically downwards as shown ... velocity of the center of the disc, when it starts rolling without slipping, will be __________________$m/s$ (round off to $2$ decimal places).
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 subjected to some internal pressure, its nominal perimeter in the cylindrical portion increased by $0.1\%$ and the corresponding ... . $100\times \left ( \bar{t} - t \right )/t$, is _______________ $\%$ (round off to $3$ decimal places).
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 internal. Gear $1$, gear $3$ and arm $OP$ are pivoted to the ground at $O$. ... $900\:\text{rpm}$ counter clockwise $\text{(ccw)}$, the magnitude of angular velocity of arm $OP$ is _____________________ $\text{rpm}$ (in integer)
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 tool is $5^{\circ}$. The uncut chip thickness and width of cut are $0.2\; mm$ ... material under this cutting condition is $1000$ $\text{MPa}$, then the cutting force is _________________ $N$ (round off to one decimal place).
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. The axial feed of the tool is $1$ $m/\text{minute}$ and the specific ... . Neglect contribution of feed force towards power. The power required to carry out this operation is _______________ $kW$ (round off to one decimal place).
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 with a mineral oil, which gives a coefficient of friction, $\mu = 0.1$. The flow stress ... $\bar{\sigma}$ is average flow stress, $L$ is roll-workpiece contact length, and $\bar{h}$ is the average sheet thickness.
Two mild steel plates of similar thickness, in butt-joint configuration, are welded by gas tungsten arc welding process using the following welding parameters. ... factor is $0.6$. The feed rate of the filler wire is _______________ $\text{mm/s}$ (round off to one decimal place).