Mechanical Engineering Gate 2013 Set-3 Questions with Answer

Ques 53 GATE 2013 SET-3

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

Ques 54 GATE 2013 SET-3

A rod of length L having uniform cross-sectional area A is subjected to a tensile force P as shown in the figure. 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

Ques 55 GATE 2013 SET-3

A planar closed kinematic chain is formed with rigid links PQ = 2.0 m, QR = 3.0 m, RS = 2.5 m and SP = 2.7 m with all revolute joints. The link to be fixed to obtain a double rocker (rocker-rocker) mechanism is

Ques 56 GATE 2013 SET-3

If two nodes are observed at a frequency of 1800 rpm during whirling of a simply supported long slender rotating shaft, the first critical speed of the shaft in rpm is

Ques 57 GATE 2013 SET-3

A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 rad/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg-m² is

Ques 58 GATE 2013 SET-3

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. If OA = 1 m, the magnitude of the absolute acceleration of the block at location A in m/s² is

Ques 59 GATE 2013 SET-3

A cylinder contains 5 m³ of an ideal gas at a pressure of 1 bar. This gas is compressed in a reversible isothermal process till its pressure increases to 5 bar. The work in kJ required for this process is

Ques 60 GATE 2013 SET-3

Specific enthalpy and velocity of steam at inlet and exit of a steam turbine, running under steady state, are as given below:

Ques 61 GATE 2013 SET-3

The pressure, temperature and velocity of air flowing in a pipe are 5 bar, 500 K and 50 m/s, respectively. The specific heats of air at constant pressure and at constant volume are 1.005 kJ/kgK and 0.718 kJ/kgK, respectively. Neglect potential energy. If the pressure and temperature of the surroundings are 1 bar and 300 K, respectively, the available energy in kJ/kg of the air stream is

Ques 62 GATE 2013 SET-3

In a simple Brayton cycle, the pressure ratio is 8 and temperatures at the entrance of compressor and turbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficiencies equal to 0.8. For the gas, assume a constant value of c_p (specific heat at constant pressure) equal to 1 kJ/kgK and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.

The power required by the compressor in kW/kg of gas flow rate is

Ques 63 GATE 2013 SET-3

In a simple Brayton cycle, the pressure ratio is 8 and temperatures at the entrance of compressor and turbine are 300 K and 1400 K, respectively. Both compressor and gas turbine have isentropic efficiencies equal to 0.8. For the gas, assume a constant value of c_p (specific heat at constant pressure) equal to 1 kJ/kgK and ratio of specific heats as 1.4. Neglect changes in kinetic and potential energies.

The thermal efficiency of the cycle in percentage (%) is

Ques 64 GATE 2013 SET-3

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

Ques 65 GATE 2013 SET-3

A single degree of freedom system having mass 1 kg and stiffness 10 kN/m initially at rest is subjected to an impulse force of magnitude 5 kN for 10^-4 seconds. The amplitude in mm of the resulting free vibration is