Mechanical Engineering Gate 2013 Set-4 Questions with Answer

Ques 27 GATE 2013 SET-4

Consider one-dimensional steady state heat conduction along x-axis (0 ≤ x ≤ L), through a plane wall with the boundary surfaces (x=0 and x=L) maintained at temperatures of 0°C and 100°C. Heat is generated uniformly throughout the wall. Choose the CORRECT statement.

Ques 28 GATE 2013 SET-4

Consider one-dimensional steady state heat conduction, without heat generation, in a plane wall; with boundary conditions as shown in the figure. 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

Ques 29 GATE 2013 SET-4

Two large diffuse gray parallel plates, separated by a small distance, have surface temperatures of 400 K and 300 K. If the emissivities of the surfaces are 0.8 and the Stefan-Boltzmann constant is 5.67×10^-8 W/m²K⁴, the net radiation heat exchange rate in kW/m² between the two plates is

Ques 30 GATE 2013 SET-4

A steel ball of diameter 60 mm is initially in thermal equilibrium at 1030°C in a furnace. It is suddenly removed from the furnace and cooled in ambient air at 30°C, with convective heat transfer coefficient h = 20 W/m²K. The thermo-physical properties of steel are: density ρ=7800 kg/m³, conductivity k=40 W/mK and specific heat c=600 J/kgK. The time required in seconds to cool the steel ball in air from 1030°C to 430°C is

Ques 31 GATE 2013 SET-4

Water (specific heat, c_p = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C. The pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux q"_w in W/m².

If q"_w = 5000 and the convection heat transfer coefficient at the pipe outlet is 1000 W/m²K, the temperature in °C at the inner surface of the pipe at the outlet is

Ques 32 GATE 2013 SET-4

Water (specific heat, c_p = 4.18 kJ/kgK) enters a pipe at a rate of 0.01 kg/s and a temperature of 20°C. The pipe, of diameter 50 mm and length 3 m, is subjected to a wall heat flux q"_w in W/m².

If q"_w = 2500x, where x is in m and in the direction of flow (x=0 at the inlet), the bulk mean temperature of the water leaving the pipe in °C is

Ques 33 GATE 2013 SET-4

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

Ques 34 GATE 2013 SET-4

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

Ques 35 GATE 2013 SET-4

A bar is subjected to fluctuating tensile load from 20 kN to 100 kN. The material has yield strength of 240 MPa and endurance limit in reversed bending is 160 MPa. According to the Soderberg principle, the area of cross-section in mm² of the bar for a factor of safety of 2 is

Ques 36 GATE 2013 SET-4

A compound gear train with gears P, Q, R and S has number of teeth 20, 40, 15 and 20, respectively. Gears Q and R are mounted on the same shaft as shown in the figure. The diameter of the gear Q is twice that of the gear R. If the module of the gear R is 2 mm, the center distance in mm between gears P and S is

Ques 37 GATE 2013 SET-4

A single riveted lap joint of two similar plates has the following geometrical and material details:

Ques 38 GATE 2013 SET-4

A single riveted lap joint of two similar plates has the following geometrical and material details:

Ques 39 GATE 2013 SET-4

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