# Mechanical Engineering - GATE 2013 Paper Solution

Question No. 1

The partial differential equation $\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=\frac{{\partial }^{2}u}{{\partial }^{2}x}$is a

Question No. 2

The eigenvalues of a symmetric matrix are all

Question No. 3

Match the CORRECT pairs.

 Numerical Integration Scheme Order of Fitting Polynomial P. Simpson’s 3/8 Rule 1. First Q. Trapezoidal Rule 2. Second R. Simpson’s 1/3 Rule 3. Third

Question No. 4

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure below. If the Young’s modulus of the material varies linearly from E1 to E2 along the length of the rod, the normal stress developed at the section-SS is

Question No. 5

Two threaded bolts A and B of same material and length are subjected to identical tensile load. If the elastic strain energy stored in bolt A is 4 times that of bolt B and the mean diameter of bolt A is 12 mm, the mean diameter of bolt B in mm is

Question No. 6

A link OB is rotating with a constant angular velocity of 2 rad/s in counter clockwise direction and a block is sliding radially outward on it with an uniform velocity of 0.75 m/s with respect to the rod, as shown in the figure below. If OA = 1 m, the magnitude of the absolute acceleration of the block at location A in m/s2 is

Question No. 7

For steady, fully developed flow inside a straight pipe of diameter D, neglecting gravity effects, the pressure drop over a length L and the wall shear stress ${\tau }_{\omega }$ are related by

Question No. 8

The pressure, dry bulb temperature and relative humidity of air in a room are 1 bar, 30°C and 70%, respectively. If the saturated steam pressure at 30°C is 4.25 kPa, the specific humidity of the room air in kg water vapour/kg dry air is

Question No. 9

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure below. The conductivity of the wall is given by k = k0 + bT  ; where k0 and b are positive constants, and T is temperature.

As x increases, the temperature gradient ( dT/dx ) will

Question No. 10

In a rolling process, the state of stress of the material undergoing deformation is

Question No. 11

Match the CORRECT pairs.

 Processes Characteristics / Applications P. Friction Welding 1. Non-consumable electrode Q. Gas Metal Arc Welding 2. Joining of thick plates R. Tungsten Inert Gas Welding 3. Consumable electrode wire S. Electroslag Welding 4. Joining of cylindrical dissimilar materials

Question No. 12

A metric thread of pitch 2 mm and thread angle 60° is inspected for its pitch diameter using 3-wire method. The diameter of the best size wire in mm is

Question No. 13

Customers arrive at a ticket counter at a rate of 50 per hr and tickets are issued in the order of their arrival. The average time taken for issuing a ticket is 1 min. Assuming that customer arrivals form a Poisson process and service times are exponentially distributed, the average waiting time in queue in min is

Question No. 14

In simple exponential smoothing forecasting, to give higher weightage to recent demand information, the smoothing constant must be close to

Question No. 15

A steel bar 200 mm in diameter is turned at a feed of 0.25 mm/rev with a depth of cut of 4 mm. The rotational speed of the workpiece is 160 rpm. The material removal rate in mm3/s is

Question No. 16

A cube shaped casting solidifies in 5 min. The solidification time in min for a cube of the same material, which is 8 times heavier than the original casting, will be

Question No. 17

For a ductile material, toughness is a measure of

Question No. 18

In order to have maximum power from a Pelton turbine, the bucket speed must be