# Mechanical Engineering - GATE 2010 Paper Solution

The parabolic arc y = $\sqrt{x}$, 1 ≤ x ≤ 2 is revolved around the x-axis. The volume of the solid of revolution is

The Blasius equation $\frac{{d}^{3}f}{d{\eta }^{3}}+\frac{f}{2}\frac{{d}^{2}f}{d{\eta }^{2}}=0$ is a

The value of the integral ${\int }_{-\infty }^{\infty }\frac{dx}{1+{x}^{2}}$ is

The modulus of the complex number $\left(\frac{3+4i}{1-2i}\right)$ is

The function y = |2 - 3x|

Mobility of a statically indeterminate structure is

There are two points P and Q on a planar rigid body. The relative velocity between the two points

The state of plane-stress at a point is given by σx =−200MPa, σy = 100MPa and $\tau$= 100MPa . The maximum shear stress in MPa is

Which of the following statements is INCORRECT?

The natural frequency of a spring-mass system on earth is ωn. The natural frequency of this system on the moon (gmoon = gearth /6) is

Tooth interference in an external involute spur gear pair can be reduced by

For the stability of a floating body, under the influence of gravity alone, which of the following is TRUE?

The maximum velocity of a one-dimensional incompressible fully developed viscous flow, between two fixed parallel plates, is 6ms-1. The mean velocity (in ms-1) of the flow is

A phenomenon is modeled using n dimensional variables with k primary dimensions. The number of non-dimensional variables is

A turbo-charged four-stroke direct injection diesel engine has a displacement volume of 0.0259m3 ( 25.9litres ) . The engine has an output of 950kW at 2200rpm. The mean effective pressure in MPa is closest to

One kilogram of water at room temperature is brought into contact with a high temperature thermal reservoir. The entropy change of the universe is

A hydraulic turbine develops 1000kW power for a head of 40m. If the head is reduced to 20m, the power developed (in kW) is

A shaft has a dimension,$?{35}^{\begin{array}{c}\begin{array}{c}-0.009\\ -0.025\end{array}\end{array}}$. The respective values of fundamental deviation and tolerance are