# GATE ME 2011

 Question 1
A streamline and an equipotential line in a flow field
 A Are parallel to each other B Are perpendicular to each other C Intersect at an acute angle D Are identical
Fluid Mechanics   Fluid Kinematics
Question 1 Explanation:
Stream line and equipotential line in a flow field are perpendicular to each other
 Question 2
If a mass of moist air in an airtight vessel is heated to a higher temperature, then
 A Specific humidity of the air increases B Specific humidity of the air decreases C Relative humidity of the air increases D Relative humidity of the air decreases
Refrigeration and Air-conditioning   Properties of Moist Air
Question 2 Explanation:
The moist air in an airtight vessel is heated to a higher temperature. This process is treated as sensible heating. In sensible heating process, the relative humidity of the air decreases with increase in dry bulb temperature at constnat specific humidity
This process is shown on psychrometic chart in Fig.
 Question 3
In a condenser of a power plant, the steam condenses at a temperature of $60^{\circ}$C. The cooling water enters at $30^{\circ}$C and leaves at $45^{\circ}$C. The logarithmic mean temperature difference (LMTD) of the condenser is
 A $16.2^{\circ}C$ B $21.6^{\circ}C$ C $30^{\circ}C$ D $37.5^{\circ}C$
Heat Transfer   Heat Exchanger
Question 3 Explanation:

\begin{aligned} \therefore \quad \mathrm{LMTD} &=\frac{\Delta T_{1}-\Delta T_{2}}{\ln \left(\frac{\Delta T_{1}}{\Delta T_{2}}\right)} \\ &=\frac{30-15}{\ln (2)}=21.64^{\circ} \mathrm{C} \end{aligned}
 Question 4
A simply supported beam PQ is loaded by a moment of 1kN-m at the mid-span of the beam as shown in the figure. The reaction forces $R_{P}$ and $R_{Q}$ at supports P and Q respectively are
 A 1kN downward, 1kN upward B 0.5kN upward, 0.5kN downward C 0.5kN downward, 0.5kNupward D 1kN upward, 1kN upward
Strength of Materials   Bending of Beams
Question 4 Explanation:

Let us assume the direction of $R_{P}$ and $R_{Q}$ as ,
upward. Now,
$\therefore \quad R_{P}+R_{Q}=0$
$\therefore$Taking moment about point Q we get:
\begin{aligned} R_{P} \times 1+1 &=0 \\ R_{P} &=-1 \mathrm{kN}\\ \therefore R_{Q}&=+1 \mathrm{kN} \end{aligned}
since our assume direction of $R_{p}$ is wrong therefore
$R_{P}=1 \mathrm{kN}$ which act in the down was direction
and $R_{Q}=1 \mathrm{kN}$ acting in upward direction.
 Question 5
A double - parallelogram mechanism is shown in the figure. Note that PQ is a single link. The mobility of the mechanism is
 A -1 B 0 C 1 D 2
Theory of Machine   Planar Mechanisms
Question 5 Explanation:
This is a special case because the link between & parallel to P and Q is redundant as its presence does not effect the mechanism. Hence the DOF is 1.
 Question 6
The maximum possible draft in cold rolling of sheet increases with the
 A Increase in coefficient of friction B Decrease in coefficient of friction C Decrease in roll radius D Increase in roll velocity
Manufacturing Engineering   Forming Process
Question 6 Explanation:
The main objective in rolling is to decrease the thickness of the metal.
The relation for the rolling is given by

$F=\mu P_r$

where,
$F=$ tangential frictional force
$\mu =$ Coefficient of friction
$P_r=$ Normal force between the roll and work piece

Now, from the increase in $\mu$, the draft in cold rolling of sheet increases.
 Question 7
The operation in which oil is permeated into the pores of a powder metallurgy product is known as
 A Mixing B Sintering C Impregnation D Infitration
Manufacturing Engineering   Forming Process
Question 7 Explanation:
Operation in which oil is permeated into the pores of powder metallurgy product is known as impregnation.
 Question 8
A hole is of dimension $\phi 9^{_{+0}^{+0.015}}$ mm. The corresponding shaft is of dimension $\phi 9^{_{+0.001}^{+0.010}}$ mm. The resulting assembly has
 A Loose running fit B Close running fit C Transition fit D Interference fit
Manufacturing Engineering   Metrology and Inspection
Question 8 Explanation:
It is case of transition fit
Since

 Question 9
Heat and work are
 A Intensive properties B Extensive properties C Point functions D Path functions
Thermodynamics   Thermodynamic System and Processes
Question 9 Explanation:
Heat and work are path function. These are not point function.
 Question 10
A column has a rectangular cross-section of 10mm x 20mm and a length of 1m. The slenderness ratio of the column is close to
 A 200 B 346 C 477 D 1000
Strength of Materials   Euler's Theory of Column
Question 10 Explanation:
Assuming both ends of column to be hinged. Given:
\begin{aligned} \qquad L_{\mathrm{eq}}&=1 \mathrm{m} \\ \text { Slenderness ratio }&=\frac{\mathrm{L}_{\mathrm{eq}}}{r_{\min }} \\ r_{\min }= \sqrt{\frac{I_{\min }}{A}}&=\frac{\sqrt{\frac{1}{12} \times(10)^{3} \times 20 \times 10^{-12}} }{10 \times 20 \times 10^{-6}}\\ &=2.88 \times 10^{-3}\\ \text{Slenderness }&=\frac{1}{2.88 \times 10^{-3}}=347.22 \approx 346 \end{aligned}
There are 10 questions to complete.