1
GATE ME 2009
MCQ (Single Correct Answer)
+1
-0.3
An analytic function of a complex variable $$z = x + i\,y$$ is expressed as
$$f\left( z \right) = u\left( {x,y} \right) + i\,\,v\,\,\left( {x,y} \right)$$ where $$i = \sqrt { - 1} .$$
If $$u=xy$$ then the expression for $$v$$ should be
A
$${{{{\left( {x + y} \right)}^2}} \over 2} + k$$
B
$${{x - {y^2}} \over 2} + k$$
C
$${{{y^2} - {x^2}} \over 2} + k$$
D
$${{{{\left( {x - y} \right)}^2}} \over 2} + k$$
2
GATE ME 2009
MCQ (Single Correct Answer)
+1
-0.3
A block weighing 981 $$N$$ is resting on a horizontal surface. The coefficient of friction between the block and the horizontal surface is $$\mu = 0.2.$$ A vertical cable attached to the block provides partial support as shown. A man can pull horizontally with a force of 100 $$N$$. What will be the tension, $$T$$ (inN) in the cable if the man is just able to move the block to the right? GATE ME 2009 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 66 English
A
176.2
B
196.0
C
481.0
D
981.0
3
GATE ME 2009
MCQ (Single Correct Answer)
+2
-0.6
A uniform rigid rod of mass $$M$$ and length $$L$$ is hinged at one end as shown in theadjacent figure. A force P is applied at a distance of $$2L/3$$ from the hinge so thatthe rod swings to the right. The reaction at the hinge is GATE ME 2009 Engineering Mechanics - Engineering Mechanics Static and Dynamics Question 32 English
A
$$-P$$
B
$$0$$
C
$$P/3$$
D
$$2p/3$$
4
GATE ME 2009
MCQ (Single Correct Answer)
+2
-0.6
You are asked to evaluate assorted fluid flows for their suitability in a given laboratory application. The following three flow choices. Expressed in terms of the two - dimensional velocity fields in the $$x-$$ $$y$$ plane, are made available.
$$P:$$ $$u = 2y,\,\,\,v = - 3x$$
$$Q:$$ $$u=3xy,$$ $$\,\,\,\,$$$$v=0$$
$$R:$$ $$u=-2x,$$ $$\,\,\,\,$$$$v=2y$$

Which flows should be recommended when the application requires the flow to be incompressible and irrotational?

A
$$P$$ and $$R$$
B
$$R$$ only
C
$$Q$$ and $$R$$
D
$$R$$ only
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