# Mechanical Engineering - GATE 2012 Paper Solution

In abrasive jet machining, as the distance between the nozzle tip and the work surface increases, the material removal rate

Match the following metal forming processes with their associated stresses in the workpiece.

 Metal forming process Type of stress 1. Coining P. Tensile 2. Wire Drawing Q. Shear 3. Blanking R. Tensile and compressive 4. Deep Drawing S. Compressive

In an interchangeable assembly, shafts of size $25.{000}^{\begin{array}{c}\begin{array}{c}+0.040\\ -0.010\end{array}\end{array}}mm$ mate with holes of size $25.{000}^{\begin{array}{c}+0.030\\ +0.020\end{array}}mm$. The maximum interference (in microns) in the assembly is

During normalizing process of steel, the specimen is heated

Oil flows through a 200 mm diameter horizontal cast iron pipe (friction factor, $f=0.0225$) of length 500 m. The volumetric flow rate is 0.2 m3/s. The head loss (in m) due to friction is (assume g = 9.81 m/s2)

For an opaque surface, the absorptivity $\left(\alpha \right)$, transmissivity $\left(\tau \right)$ and reflectivity $\left(\rho \right)$ are related by the equation:

Steam enters an adiabatic turbine operating at steady state with an enthalpy of 3251.0 kJ/kg and leaves as a saturated mixture at 15 kPa with quality (dryness fraction) 0.9. The enthalpies of the saturated liquid and vapor at 15 kPa are hf = 225.94 kJ/kg and hg = 2598.3 kJ/kg respectively. The mass flow rate of steam is 10 kg/s. Kinetic and potential energy changes are negligible. The power output of the turbine in MW is

The following are the data for two crossed helical gears used for speed reduction:
Gear I : Pitch circle diameter in the plane of rotation 80 mm and helix angle 30º
Gear II : Pitch circle diameter in the plane of rotation 120 mm and helix angle 22.5º
If the input speed is 1440 rpm, the output speed in rpm is

A solid disc of radius $r$ rolls without slipping on a horizontal floor with angular velocity $\alpha$ and angular acceleration $\alpha$. The magnitude of the acceleration of the point of contact on the disc is

A thin walled spherical shell is subjected to an internal pressure. If the radius of the shell is increased by 1% and the thickness is reduced by 1%, with the internal pressure remaining the same, the percentage change in the circumferential (hoop) stress is

The area enclosed between the straight line y = x and the parabola y = x2 in the x-y plane is

Consider the function $f\left(x\right)=\left|x\right|$ in the interval $-1\le x\le 1$. At the point $x=0$, $f\left(x\right)$ is

Which one of the following is NOT a decision taken during the aggregate production planning stage?

$\underset{x\to 0}{\mathrm{lim}}\left(\frac{1-\mathrm{cos}x}{{x}^{2}}\right)$ is

A CNC vertical milling machine has to cut a straight slot of 10 mm width and 2 mm depth by a cutter of 10 mm diameter between points (0, 0) and (100, 100) on the XY plane (dimensions in mm). The feed rate used for milling is 50 mm/min. Milling time for the slot (in seconds) is

A solid cylinder of diameter 100 mm and height 50 mm is forged between two frictionless flat dies to a height of 25 mm. The percentage change in diameter is

The velocity triangles at the inlet and exit of the rotor of a turbomachine are shown. V denotes the absolute velocity of the fluid, W denotes the relative velocity of the fluid and U denotes the blade velocity. Subscripts 1 and 2 refer to inlet and outlet respectively. If V2 = W1 and V1 = W2, then the degree of reaction is

An ideal gas of mass m and temperature T1 undergoes a reversible isothermal process from an initial pressure P1 to final pressure P2. The heat loss during the process is Q. The entropy change $\Delta$S of the gas is