Recent questions tagged numerical-answers

Evaluation of $\int_2^4 x^3 dx$ using a $2$-equal-segment trapezoidal rule gives a value of _______

A block of mass $10$ kg rests on a horizontal floor. The acceleration due to gravity is $9.81 \: m/s^2$. The coefficient of static friction between the floor and the bloc...

A cylindrical rod of diameter $10$ mm and length $0.1$m fixed at one end. The other end is twisted by an angle of $10^{\circ}$ by applying a torque. If the maximum shear ...

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...

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...

In ASA system, the side cutting and end cutting edge angles of a sharp turning tool are $45^{\circ}$ and $10^{\circ}$, respectively. The feed during cylindrical turning i...

Taylor’s tool life equation is given by $VT^n=C$, where $V$ is in $m/min$ and $T$ is in $min$. In a turning operation, two tools $X$ and $Y$ are used. For tool $X$, $n=0....

Five jobs $(J1, J2, J3, J4$ and $J5)$ need to be processes in a factory. Each job can be assigned to any of the five different machines $(M1, M2, M3, M4$ and $M5)$. The t...

A project consists of six activities. The immediate predecessor of each activity and the estimated duration is also provided in the table below:$\begin{array}{|c|c|c|} \h...

A vehicle powered by a spark ignition engine follows air standard Otto cycle ($\gamma =1.4$). The engine generates $70$ kW while consuming $10.3$ kg/hr of fuel. The calor...

Steam in the condenser of a thermal power plant is to be condensed at a temperature of $30^{\circ}C$ with cooling water which enters the tubes of the condenser at $14^{\c...

A welding operation is being performed with voltage $= 30 \: V$ and current =$100 \: A$. The cross-sectional area of the weld bead is $20 \: mm^2$. The work-piece and fil...

A circular hole of $25 \: mm$ diameter and depth of $20 \: mm$ is machined by EDM process. The material removal rate (in $mm^3/min$) is expressed as $$ 4 \times 10^4 \: I...