1
GATE ME 2017 Set 2
Numerical
+2
-0
The radius of gyration of a compound pendulum about the point of suspension is $$100$$ mm. The distance between the point of suspension and the centre of mass is $$250$$ mm. Considering the acceleration due to gravity as $$9.81$$ m/s2, the natural frequency (in radian/s) of the compound pendulum is _________.
2
GATE ME 2017 Set 2
+2
-0.6
The volume and temperature of air (assumed to be an ideal gas) in a closed vessel is $$2.87{m^3}$$ and $$300$$ $$K,$$ respectively. The gauge pressure indicated by a manometer fitted to the wall of the vessel is $$0.5$$ bar. If the gas constant of air is
$$R =287J/kgK$$ and the atmospheric pressure is $$1$$ bar, the mass of air (in $$kg$$) in the vessel is
A
$$1.67$$
B
$$3.33$$
C
$$5.00$$
D
$$6.66$$
3
GATE ME 2017 Set 2
+2
-0.6
A calorically perfect gas (specific heat at constant pressure $$1000$$$$J/kg.K$$) enters and leaves a gas turbine with the same velocity. The temperatures of the gas at turbine entry and exit are $$1100K$$ and $$400K.$$ respectively. The power produced is $$4.6MW$$ and heat escapes at the rate of $$300kJ/s$$ through the turbine casing. The mass flow rate of the gas (in $$kg/s$$) through the turbine is.
A
$$6.14$$
B
$$7.00$$
C
$$7.50$$
D
$$8.00$$
4
GATE ME 2017 Set 2
+1
-0.3
A mass $$m$$ of a perfect gas at pressure $${p_1}$$ and volume $${V_1}$$ undergoes an isothermal process. The final pressure is $${p_2}$$ and volume is $${V_2}.$$ The work done on the system is considered positive. If $$R$$ is the gas constant and $$T$$ is the temperature, then the work done in the process is
A
$${p_1}{V_1}\ell n{{{V_2}} \over {{V_1}}}$$
B
$$- {p_1}{V_1}\ell n{{{p_1}} \over {{p_2}}}$$
C
$$RT\ell n{{{V_2}} \over {{V_1}}}$$
D
$$- mRT\ell n{{{p_2}} \over {{p_1}}}$$
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