ME GATE 2011 - Online Test
Q1. An ideal Brayton cycle, operating between the pressure limits of 1 bar and 6 bar,
has minimum and maximum temperatures of 300K and 1500K. The ratio of
specific heats of the working fluid is 1.4. The approximate final temperatures in
Kelvin at the end of the compression and expansion processes are respectively
Answer : Option A
Explaination / Solution:
Ideal Brayton cycle
At the end of compression, temperature.
Q2. For the four-bar linkage shown in the figure, the angular velocity of link AB is 1
rad/s. the length of link CD is 1.5 times the length of link AB. In the configuration
shown, the angular velocity of link CD in rad/s is
Answer : Option D
Explaination / Solution:
For the given configuration
Q3. In an experimental set-up, air flows between two stations P and Q adiabatically.
The direction of flow depends on the pressure and temperature conditions
maintained at P and Q. The conditions at station P are 150kPa and 350K. The
temperature at station Q is 300K.
The following are the properties and relations pertaining to air:
Specific heat at constant pressure, Cp = 1.005kJ / kgK;
Specific heat at constant volume, Cv = 0.718kJ / kgK;
Characteristic gas constant, R = 0.287kJ / kgK
Enthalpy, h = CpT
Internal energy, u = CvT
If the air has to flow from station P to station Q, the maximum possible value of
pressure in kPa at station Q is close to
Answer : Option B
Explaination / Solution:
To cause the flow from P to Q, change in entropy (SP - SQ) should be
greater than zero 
∴ The maximum value of pressure at Q = 87 kPa
Q4. A stone with mass of 0.1kg is catapulted as shown in the figure. The total force Fx (in N) exerted by the rubber band as a function of distance x (in m) is given by F = 300x2. If the stone is displaced by 0.1m from the un-stretched position
(x=0) of the rubber band, the energy stored in the rubber band is
Answer : Option B
Explaination / Solution:
Energy stored in the bar = W.D. by the stone
Q5. In an experimental set-up, air flows between two stations P and Q adiabatically. The direction of flow depends on the pressure and temperature conditions maintained at P and Q. The conditions at station P are 150kPa and 350K. The temperature at station Q is 300K.
The following are the properties and relations pertaining to air:
Specific heat at constant pressure, Cp = 1.005kJ / kgK;
Specific heat at constant volume, Cv = 0.718kJ / kgK;
Characteristic gas constant, R = 0.287kJ / kgK
Enthalpy, h = CpT
Internal energy, u = CvT
If the pressure at station Q is 50kPa, the change in entropy (SQ - SP) in kJ/kgK is
Answer : Option C
Explaination / Solution:
No Explaination.
Q6. A mass of 1kg is attached to two identical springs each with stiffness k = 20kN/m
as shown in the figure. Under frictionless condition, the natural frequency of the
system in Hz is close to
Answer : Option A
Explaination / Solution:
Natural frequency of the system
Q7. The temperature and pressure of air in a large reservoir are 400K and 3 bar
respectively. A converging–diverging nozzle of exit area 0.005m2 is fitted to the
wall of the reservoir as shown in the figure. The static pressure of air at the exit
section for isentropic flow through the nozzle is 50kPa. The characteristic gas
constant and the ratio of specific heats of air are 0.287kJ/kgK and 1.4
respectively
The density of air in kg/ m3 at the nozzle exit is
Answer : Option C
Explaination / Solution:
Given data:
T1 = 400k, P1 = 300 kPa, P2 = 50kPa, R = 0.289kJ / kgK
v = 1.4, A2 = 0.005m2
The happened process from entrance to exit is isentropic process, therefore
Q8. The shear strength of a sheet metal is 300MPa. The blanking force required to
produce a blank of 100mm diameter from a 1.5 mm thick sheet is close to
Answer : Option C
Explaination / Solution:
Blanking force = τ . As = 300 × πdt = 300 × π × 100 × 1.5 = 141 kN
Q9. The temperature and pressure of air in a large reservoir are 400K and 3 bar respectively. A converging–diverging nozzle of exit area 0.005m2 is fitted to the wall of the reservoir as shown in the figure. The static pressure of air at the exit section for isentropic flow through the nozzle is 50kPa. The characteristic gas constant and the ratio of specific heats of air are 0.287kJ/kgK and 1.4 respectively
The mass flow rate of air through the nozzle in kg/s is
Answer : Option D
Explaination / Solution:
No Explaination.
Q10. A disc of mass m is attached to a spring of stiffness k as shown in the figure. The
disc rolls without slipping on a horizontal surface. The natural frequency of
vibration of the system is 
Answer : Option C
Explaination / Solution:
No Explaination.
