12583 + Mcqs in Physics Page 48 McqOptions

2351.	One liter of oxygen at a pressure of 1 atm, and 2 liters of nitrogen at a pressure of 0.5 atm. Are introduced in the vessel of 1 liter capacity, without any change in temperature. The total pressure would be
A.	1.5 atm.
B.	0.5 atm.
C.	2.0 atm.
D.	1.0 atm.
Answer» D. 1.0 atm.

Discussion

2352.	Which of the following will have maximum total kinetic energy at temperature 300K?
A.	\[1kg{{H}_{2}}\]
B.	\[1kgHe\]
C.	\[\frac{1}{2}1kg{{H}_{2}}+\frac{1}{2}1kgHe\]
D.	\[\frac{1}{4}1kg{{H}_{2}}+\frac{3}{4}1kgHe\]
Answer» B. \[1kgHe\]

Discussion

2353.	If the molecules in a tank of hydrogen have the same RMS speed as the molecules in another tank of oxygen, we may be sure that
A.	the pressures are the same
B.	the hydrogen is at the higher temperature
C.	the temperatures are the same
D.	the oxygen is at the higher temperature
Answer» E.

Discussion

2354.	Air is pumped into an automobile tube up to a pressure of 200 kPa in the morning when the air temperature is \[22{}^\circ C.\] During the day, temperature rises to \[42{}^\circ C\] and the tube expands by 2%. The pressure of the air in the tube at this temperature, will be approximately
A.	212 kPa
B.	209 kPa
C.	206 kPa
D.	200 kPa
Answer» C. 206 kPa

Discussion

2355.	A gas at \[27{}^\circ C\] temperature and 30 atmospheric pressure is allowed to expand to the atmospheric pressure. If the volume becomes 10 times its initial volume, then the final temperature becomes
A.	\[100{}^\circ C\]
B.	\[173{}^\circ C\]
C.	\[273{}^\circ C\]
D.	\[-173{}^\circ C\]
Answer» E.

Discussion

2356.	The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be where R is the gas constant.
A.	\[PV=(5/16)RT~~\]
B.	\[PV=(5/32)RT\]
C.	\[PV=5RT~\]
D.	\[PV=(5/2)RT\]
Answer» C. \[PV=5RT~\]

Discussion

2357.	One mole of an ideal gas undergoes a process\[P=\frac{{{P}_{0}}}{1+{{\left( \frac{{{V}_{0}}}{V} \right)}^{2}}}\] Here \[{{P}_{0}}\] and \[{{V}_{0}}\] are constant. Change in temperature of the gas when volume is changed from \[V={{V}_{0}}\] to \[V=2{{V}_{0}}\]
A.	\[\frac{-2{{P}_{0}}{{V}_{0}}}{5R}\]
B.	\[\frac{11{{P}_{0}}{{V}_{0}}}{10R}\]
C.	\[\frac{-5{{P}_{0}}{{V}_{0}}}{10R}\]
D.	\[{{P}_{0}}{{V}_{0}}\]
Answer» C. \[\frac{-5{{P}_{0}}{{V}_{0}}}{10R}\]

Discussion

2358.	In the given (V - T) diagram, what is the relation between pressure \[{{P}_{1}}\] and\[{{P}_{2}}\]?
A.	\[{{P}_{2}}>{{P}_{1}}\]
B.	\[{{P}_{2}}<{{P}_{1}}\]
C.	Cannot be predicted
D.	\[{{P}_{2}}={{P}_{1}}\]
Answer» C. Cannot be predicted

Discussion

2359.	The maximum attainable temperature of ideal gas in the process \[P={{P}_{0}}-\alpha {{V}^{2}}\] where \[{{P}_{0}}\]and \[\alpha \] are +ve constants.
A.	\[\frac{2{{P}_{0}}}{3nR}{{\left( \frac{{{P}_{0}}}{3\alpha } \right)}^{1/2}}\]
B.	\[\frac{{{P}_{0}}}{2nR}{{\left( \frac{2{{P}_{0}}}{3\alpha } \right)}^{1/2}}\]
C.	\[\frac{2nR}{{{P}_{0}}}{{\left( \frac{2{{P}_{0}}}{3\alpha } \right)}^{1/2}}\]
D.	\[\frac{2{{P}_{0}}}{nR}{{\left( \frac{{{P}_{0}}}{2\alpha } \right)}^{1/2}}\]
Answer» B. \[\frac{{{P}_{0}}}{2nR}{{\left( \frac{2{{P}_{0}}}{3\alpha } \right)}^{1/2}}\]

Discussion

2360.	An air bubble of volume \[{{v}_{0}}\] is released by a fish at a depth h in a lake. The bubble rises to the standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density of water is p)
A.	\[{{v}_{0}}\]
B.	\[{{v}_{0}}\left( \rho gh/p \right)\]
C.	\[{{N}_{2}}\]
D.	\[{{v}_{0}}\left( 1+\frac{\rho gh}{p} \right)\]
Answer» E.

Discussion

2361.	A closed hollow insulated cylinder is filled with gas at \[0{}^\circ C\]and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas on one side of the piston is heated to \[100{}^\circ C.\]If the piston moves 5 cm, the length of the hollow cylinder is
A.	13.65 cm
B.	27.3 cm
C.	38.6 cm
D.	64.6 cm
Answer» E.

Discussion

2362.	The mean free path of molecules of a gas, (radius
A.	\[{{r}^{3}}\]
B.	\[{{r}^{2}}\]
C.	\[r\]
D.	\[\sqrt{r}\]
Answer» C. \[r\]

Discussion

2363.	Three containers of the same volume contain three different gases. The masses of the molecules are \[{{m}_{1}},{{m}_{2}}\]and \[{{m}_{3}}\]the number of\[{{N}_{1}}\], \[{{N}_{2}}\] and \[{{N}_{3}}.\] The gas pressure in the containers \[{{P}_{1}},{{P}_{2}}\] and \[{{P}_{3}}\] respectively. All the gases are now mixed and put in one of these containers. The pressure P of the mixture will be
A.	\[P<\left( {{P}_{1}}+{{P}_{2}}+{{P}_{3}} \right)\]
B.	\[P=\frac{{{P}_{1}}+{{P}_{2}}+{{P}_{3}}}{3}\]
C.	\[P={{P}_{1}}+{{P}_{2}}+{{P}_{3}}\]
D.	\[P>\left( {{P}_{1}}+{{P}_{2}}+{{P}_{3}} \right)\]
Answer» D. \[P>\left( {{P}_{1}}+{{P}_{2}}+{{P}_{3}} \right)\]

Discussion

2364.	The temperature of an air bubble while rising from bottom to surface of a lake remains constant but its diameter is doubled if the pressure on the surface is equal to h meter of mercury column and relative density of mercury is \[\rho \] then the depth of lake in meter is
A.	\[2\rho h\]
B.	\[4\rho h\]
C.	\[8\rho h\]
D.	\[7\rho h\]
Answer» E.

Discussion

2365.	The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are \[6.21\text{ }\times \text{ }{{10}^{-21}}\text{ }J\] and 484 m/s respectively The corresponding values at 600 K are nearly (assuming ideal gas behavior)
A.	\[12.42\times {{10}^{-21}}J,928m/s\]
B.	\[8.78\times {{10}^{-21}}J,684m/s\]
C.	\[6.21\times {{10}^{-21}}J,968m/s\]
D.	\[12.42\times {{10}^{-21}}J,684m/s\]
Answer» E.

Discussion

2366.	A perfect gas at \[27{}^\circ C\] is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to
A.	(a)\[327{}^\circ C\]
B.	\[200{}^\circ C\]
C.	\[54{}^\circ C\]
D.	\[300{}^\circ C\]
Answer» B. \[200{}^\circ C\]

Discussion

2367.	At \[10{}^\circ C\] the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At \[110{}^\circ C\]this ratio is:
A.	x
B.	\[\frac{383}{283}x\]
C.	\[\frac{10}{110}x\]
D.	\[\frac{283}{383}x\]
Answer» E.

Discussion

2368.	The average translational kinetic energy of \[{{O}_{2}}\](relative molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of \[{{N}_{2}}\] (relative molar mass 28) molecules in eV at the same temperature is
A.	0.0015
B.	0.003
C.	0.048
D.	0.768
Answer» D. 0.768

Discussion

2369.	The figure shows graph of pressure and volume of a gas at two different temperatures \[{{T}_{1}}\]and\[{{T}_{2}}\]. Which of the following inferences is correct?
A.	\[{{T}_{1}}>{{T}_{2}}\]
B.	\[{{T}_{1}}={{T}_{2}}\]
C.	\[{{T}_{1}}<{{T}_{2}}\]
D.	None of these
Answer» D. None of these

Discussion

2370.	The absolute gas temperature at which the root mean square speed of helium molecules exceeds their most probable speed by 200 m/s is
A.	110.2 K
B.	90.2 K
C.	190.2 K
D.	100.2 K
Answer» D. 100.2 K

Discussion

2371.	A balloon contains \[1500\text{ }{{m}^{3}}\] of helium at \[27{}^\circ C\]and 4 atmospheric pressure. The volume of helium at \[-3{}^\circ C\] temperature and 2 atmospheric pressure will,
A.	\[1500{{m}^{3}}~\]
B.	\[~1700{{m}^{3}}\]
C.	\[1900{{m}^{3}}\]
D.	\[~2700{{m}^{3}}\]
Answer» E.

Discussion

2372.	Boyle' law is applicable for an
A.	adiabatic process.
B.	isothermal process.
C.	isobaric process.
D.	isochoric process
Answer» C. isobaric process.

Discussion

2373.	The density (p)versus pressure (P) of a given mass of an ideal gas is shown at two temperatures\[~{{T}_{1}}\] and \[~{{T}_{2}}\] Then relation between \[~{{T}_{1}}\] and \[~{{T}_{2}}\] may be
A.	\[{{T}_{1}}>{{T}_{2}}\]
B.	\[{{T}_{2}}>{{T}_{1}}\]
C.	\[{{T}_{1}}={{T}_{2}}\]
D.	All the three are possible
Answer» C. \[{{T}_{1}}={{T}_{2}}\]

Discussion

2374.	N molecules each of mass m of a gas A and 2N molecules each of mass 2m of gas B are contained in the same vessel which is maintained at temperature T. The mean square velocity of molecules of B type is \[{{v}^{2}}\] and the mean square rectangular component of the velocity of A type is denoted by \[{{\omega }^{2}}.\] Then \[6.21\text{ }\times \text{ }{{10}^{-21}}\text{ }J\]is
A.	2
B.	1
C.	1/3
D.	44257
Answer» E.

Discussion

2375.	Three closed vessels A, B and C are at the same temperature T and contain gases which obey the Maxwellian distribution of velocities. Vessel A contain only\[{{O}_{2}}\], B only \[{{N}_{2}}\] and C a mixture of equal quantities of \[{{O}_{2}}\] and \[{{N}_{2}}\]. If the average speed of the \[{{O}_{2}}\] molecules in vessel A is that of the \[{{N}_{2}}\] molecules in vessel B is \[{{v}_{2}},\] the average speed of the \[{{O}_{2}}\] molecules in vessel C is
A.	\[\frac{{{v}_{1}}+{{v}_{2}}}{2}\]
B.	\[{{v}_{1}}\]
C.	\[{{\left( {{v}_{1}}.{{v}_{2}} \right)}^{\frac{1}{2}}}\]
D.	\[\sqrt{\frac{3kT}{M}}\]
Answer» C. \[{{\left( {{v}_{1}}.{{v}_{2}} \right)}^{\frac{1}{2}}}\]

Discussion

2376.	In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as\[{{\text{T}}^{\text{q}}}\]. A good estimate for q is:
A.	\[\frac{1}{2}\]
B.	2
C.	1
D.	\[\frac{1}{4}\]
Answer» D. \[\frac{1}{4}\]

Discussion

2377.	One gram mole of nitrogen at \[27{}^\circ C\]and 1 aim pressure is contained in a vessel and the molecules are moving with their rms speed. The number of collisions per second which the vessel's wall is
A.	\[2\times {{10}^{27}}\]
B.	\[~2\times {{10}^{20}}\]
C.	\[2\times {{10}^{10}}\]
D.	\[~2\times {{10}^{24}}\]
Answer» B. \[~2\times {{10}^{20}}\]

Discussion

2378.	Four molecules have speeds 2 km/sec, 3 km/sec, 4 km/sec and 5 km/sec. The root mean square speed of these molecules (in km/sec) is
A.	\[\sqrt{54/4}\]
B.	\[\sqrt{54/2}\]
C.	3.5
D.	\[3\sqrt{3}\]
Answer» B. \[\sqrt{54/2}\]

Discussion

2379.	Five gas molecules chosen at random are found to have speeds of 500, 600, 700, 800 and 900 m/s
A.	the root mean square speed and the average
B.	the root mean square speed is 14 m/s higher than the average speed.
C.	the root mean square speed is 14 m/s lower than the average speed.
D.	the root mean square speed is \[\sqrt{14}\text{ m/s}\]higher than the average speed.
Answer» C. the root mean square speed is 14 m/s lower than the average speed.

Discussion

2380.	Relation between pressure (P) and energy (E) of gas is
A.	\[P=\frac{2}{3}E\]
B.	\[P=\frac{1}{3}E\]
C.	\[P=\frac{1}{2}E\]
D.	\[P=3E\]
Answer» B. \[P=\frac{1}{3}E\]

Discussion

2381.	Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative
A.	\[{{V}_{1}}={{V}_{2}};{{V}_{3}}={{V}_{4}}\text{ and }{{V}_{2}}>{{V}_{3}}\]
B.	\[{{V}_{1}}={{V}_{2}};{{V}_{3}}={{V}_{4}}\text{ and }{{V}_{2}}<{{V}_{3}}\]
C.	\[{{V}_{1}}={{V}_{2}}={{V}_{3}}={{V}_{4}}\]
D.	\[{{V}_{4}}>{{V}_{3}}>{{V}_{2}}>{{V}_{1}}\]
Answer» B. \[{{V}_{1}}={{V}_{2}};{{V}_{3}}={{V}_{4}}\text{ and }{{V}_{2}}<{{V}_{3}}\]

Discussion

2382.	The quantity of gas in a closed vessel is halved and the velocities of its molecules are doubled. The final pressure of the gas will be
A.	P
B.	2P
C.	P/2
D.	4P
Answer» C. P/2

Discussion

2383.	Modern vacuum pumps can evacuate a vessel down to a pressure of \[4.0\times {{10}^{-15}}\text{ }atm.\]at room temperature (300 K). Taking , \[1\text{ }atm=105\text{ }Pa\]and \[{{N}_{avogadro}}=6\times {{10}^{23}}mol{{e}^{-1}},\] the mean distance between molecules of gas in an evacuated vessel will be of the order of:
A.	0.2 urn
B.	0.2 mm
C.	0.2 cm
D.	0.2 nm
Answer» C. 0.2 cm

Discussion

2384.	At what temperature is the r. m. s velocity of a hydrogen molecule equal to that of an oxygen molecule at \[47{}^\circ C\]?
A.	80 K
B.	-73 K
C.	3 K
D.	20 K
Answer» E.

Discussion

2385.	A nitrogen molecule has some rms speed at \[0{}^\circ C\]on the surface of the earth. With this speed, it goes straight up. If there is no collisions with other molecules, the molecule will rise up to a height of
A.	82 km
B.	12.4 km
C.	10.6 km
D.	152 km
Answer» C. 10.6 km

Discussion

2386.	The density of a gas is \[6\times {{10}^{-2}}kg/{{m}^{3}}\] and the root mean square velocity of the gas molecules is 500 m/s. The pressure exerted by the gas on the walls of the vessel is
A.	\[5\times {{10}^{3}}N/{{m}^{2}}\]
B.	\[1.1\times {{10}^{-4}}N/{{m}^{2}}\]
C.	\[0.83\times {{10}^{-4}}N/{{m}^{2}}~\]
D.	\[30N/{{m}^{2}}\]
Answer» B. \[1.1\times {{10}^{-4}}N/{{m}^{2}}\]

Discussion

2387.	Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of \[{{V}_{rms}}\] of molecules and speed of sound in mixture?
A.	\[\sqrt{3/2}\]
B.	\[\sqrt{2}\]
C.	\[\sqrt{2/3}\]
D.	\[\sqrt{3}\]
Answer» C. \[\sqrt{2/3}\]

Discussion

2388.	The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is v, at 480 K it becomes
A.	4v
B.	2v
C.	v/2
D.	v/4
Answer» C. v/2

Discussion

2389.	Why does the pressure of an ideal gas increase when it is heated at constant volume?
A.	The gas molecules expand
B.	The molecules move at the same speed, but
C.	The molecules move faster and hit the walls more often
D.	The number of molecules of gas increases
Answer» D. The number of molecules of gas increases

Discussion

2390.	Helium gas is filled in a closed vessel (having negligible thermal expansion coefficient) when it is heated from 300 K to 600 K, then average kinetic energy of helium atom will be
A.	\[\sqrt{2}\] times
B.	2 times
C.	unchanged
D.	half
Answer» C. unchanged

Discussion

2391.	The pressure of a gas is raised from \[27{}^\circ C\]to \[927{}^\circ C.\]The root mean square speed is
A.	\[\sqrt{\left( 927/27 \right)}\] times the earlier value
B.	remain the same
C.	gets halved
D.	get doubled
Answer» E.

Discussion

2392.	Consider a gas with density \[\rho \] and \[\overline{c}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity, then the pressure exerted by the gas is
A.	\[\frac{1}{3}\rho {{\bar{c}}^{2}}\]
B.	\[\frac{1}{3}\rho {{\left( c+\nu \right)}^{2}}\]
C.	\[\frac{1}{3}\rho {{\left( \bar{c}-\nu \right)}^{2}}\]
D.	\[\frac{1}{3}\rho {{\left( {{{\bar{c}}}^{2}}-\nu \right)}^{2}}\]
Answer» B. \[\frac{1}{3}\rho {{\left( c+\nu \right)}^{2}}\]

Discussion

2393.	At room temperature a diatomic gas is found to have an r. m. s. speed of \[1930\text{ }m{{s}^{-1}}\]. The gas is:
A.	\[{{H}_{2}}\]
B.	\[C{{l}_{2}}\]
C.	\[{{O}_{2}}\]
D.	\[{{F}_{2}}\]
Answer» B. \[C{{l}_{2}}\]

Discussion

2394.	For a gas sample with Np number of molecules, function N(V) is given by: \[N\left( V \right)=\frac{dN}{dV}=\left[ \frac{3{{F}_{0}}}{V_{0}^{3}} \right]{{V}^{2}}\] for \[0\le V\le {{V}_{0}}\]and \[N\left( V \right)=0\]for \[V>{{V}_{0}}\] Where \[dN\] is number of molecules in speed range V to \[V+dV.\]The rms speed of the gas molecule is
A.	\[\sqrt{\frac{2}{5}}{{V}_{0}}\]
B.	\[\sqrt{\frac{3}{5}}{{V}_{0}}\]
C.	\[\sqrt{2}{{V}_{0}}\]
D.	\[\sqrt{3}{{V}_{0}}\]
Answer» C. \[\sqrt{2}{{V}_{0}}\]

Discussion

2395.	In kinetic theory of gases, which of the following statement regarding elastic collisions of the molecules is wrong?
A.	Kinetic energy is lost in collisions
B.	Kinetic energy remains constant in collision
C.	Momentum is conserved in collision
D.	Pressure of the gas remains constant in collisions
Answer» D. Pressure of the gas remains constant in collisions

Discussion

2396.	The velocity of sound in air is \[332\text{ }m\text{ }{{s}^{-1}}\] at NTP. Find the rms speed of air molecules at NTP. \[\left( \gamma =1.41 \right)\]
A.	\[484\text{ }m{{s}^{-1}}\]
B.	\[418\text{ }m{{s}^{-1}}\]
C.	\[248\text{ }m{{s}^{-1}}\]
D.	\[382\text{ }m{{s}^{-1}}\]
Answer» B. \[418\text{ }m{{s}^{-1}}\]

Discussion

2397.	A system consists of two stars of equal masses that revolve in a circular orbit about a centre of mass midway between them. Orbital speed of each star is v and period is T. Find the mass M of each star (G is gravitational constant)
A.	\[\frac{2G{{v}^{3}}}{\pi T}\]
B.	\[\frac{{{v}^{3}}T}{\pi G}\]
C.	\[\frac{{{v}^{3}}T}{2\pi G}\]
D.	\[\frac{2T{{v}^{3}}}{\pi G}\]
Answer» E.

Discussion

2398.	Infinite number of masses, each 1 kg are placed along the x-axis \[\operatorname{at} x=\pm 1 m, \pm 2m, \pm 4m, \pm \]\[8m, \pm 16M\ldots \] the magnitude of the resultant gravitational potential in terms of gravitational constant G at the or g in \[(x=0)\] is
A.	G/2
B.	G
C.	2G
D.	4G
Answer» D. 4G

Discussion

2399.	The gravitational field due to a mass distribution is \[\operatorname{E}=K/{{x}^{3}}\]in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is
A.	\[K/x\]
B.	\[K/2x\]
C.	\[\operatorname{K}/{{x}^{2}}\]
D.	\[\operatorname{K}/2{{x}^{2}}\]
Answer» E.

Discussion

2400.	The gravitational field in a region is given by\[\vec{g} =5N/kg\hat{i}+12N/kg\hat{j}\]. The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point \[(7m,-3m)\] is:
A.	\[71\text{ }J\]
B.	\[13\sqrt{58}J\]
C.	\[-71\text{ }J\]
D.	\[1\text{ }J\]
Answer» E.

Discussion

Explore topic-wise MCQs in Joint Entrance Exam - Main (JEE Main).

One liter of oxygen at a pressure of 1 atm, and 2 liters of nitrogen at a pressure of 0.5 atm. Are introduced in the vessel of 1 liter capacity, without any change in temperature. The total pressure would be

Which of the following will have maximum total kinetic energy at temperature 300K?

If the molecules in a tank of hydrogen have the same RMS speed as the molecules in another tank of oxygen, we may be sure that

Air is pumped into an automobile tube up to a pressure of 200 kPa in the morning when the air temperature is \[22{}^\circ C.\] During the day, temperature rises to \[42{}^\circ C\] and the tube expands by 2%. The pressure of the air in the tube at this temperature, will be approximately

A gas at \[27{}^\circ C\] temperature and 30 atmospheric pressure is allowed to expand to the atmospheric pressure. If the volume becomes 10 times its initial volume, then the final temperature becomes

The equation of state for 5 g of oxygen at a pressure P and temperature T, when occupying a volume V, will be where R is the gas constant.

One mole of an ideal gas undergoes a process\[P=\frac{{{P}_{0}}}{1+{{\left( \frac{{{V}_{0}}}{V} \right)}^{2}}}\] Here \[{{P}_{0}}\] and \[{{V}_{0}}\] are constant. Change in temperature of the gas when volume is changed from \[V={{V}_{0}}\] to \[V=2{{V}_{0}}\]

In the given (V - T) diagram, what is the relation between pressure \[{{P}_{1}}\] and\[{{P}_{2}}\]?

The maximum attainable temperature of ideal gas in the process \[P={{P}_{0}}-\alpha {{V}^{2}}\] where \[{{P}_{0}}\]and \[\alpha \] are +ve constants.

An air bubble of volume \[{{v}_{0}}\] is released by a fish at a depth h in a lake. The bubble rises to the standard atmospheric pressure above the lake. The volume of the bubble just before touching the surface will be (density of water is p)

The mean free path of molecules of a gas, (radius

The temperature of an air bubble while rising from bottom to surface of a lake remains constant but its diameter is doubled if the pressure on the surface is equal to h meter of mercury column and relative density of mercury is \[\rho \] then the depth of lake in meter is

The average translational energy and the rms speed of molecules in a sample of oxygen gas at 300 K are \[6.21\text{ }\times \text{ }{{10}^{-21}}\text{ }J\] and 484 m/s respectively The corresponding values at 600 K are nearly (assuming ideal gas behavior)

A perfect gas at \[27{}^\circ C\] is heated at constant pressure so as to double its volume. The final temperature of the gas will be, close to

At \[10{}^\circ C\] the value of the density of a fixed mass of an ideal gas divided by its pressure is x. At \[110{}^\circ C\]this ratio is:

The average translational kinetic energy of \[{{O}_{2}}\](relative molar mass 32) molecules at a particular temperature is 0.048 eV. The translational kinetic energy of \[{{N}_{2}}\] (relative molar mass 28) molecules in eV at the same temperature is

The figure shows graph of pressure and volume of a gas at two different temperatures \[{{T}_{1}}\]and\[{{T}_{2}}\]. Which of the following inferences is correct?

The absolute gas temperature at which the root mean square speed of helium molecules exceeds their most probable speed by 200 m/s is

A balloon contains \[1500\text{ }{{m}^{3}}\] of helium at \[27{}^\circ C\]and 4 atmospheric pressure. The volume of helium at \[-3{}^\circ C\] temperature and 2 atmospheric pressure will,

Boyle' law is applicable for an

The density (p)versus pressure (P) of a given mass of an ideal gas is shown at two temperatures\[~{{T}_{1}}\] and \[~{{T}_{2}}\] Then relation between \[~{{T}_{1}}\] and \[~{{T}_{2}}\] may be

In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as\[{{\text{T}}^{\text{q}}}\]. A good estimate for q is:

One gram mole of nitrogen at \[27{}^\circ C\]and 1 aim pressure is contained in a vessel and the molecules are moving with their rms speed. The number of collisions per second which the vessel's wall is

Four molecules have speeds 2 km/sec, 3 km/sec, 4 km/sec and 5 km/sec. The root mean square speed of these molecules (in km/sec) is

Five gas molecules chosen at random are found to have speeds of 500, 600, 700, 800 and 900 m/s

Relation between pressure (P) and energy (E) of gas is

Pressure versus temperature graph of an ideal gas of equal number of moles of different volumes are plotted as shown in figure. Choose the correct alternative

The quantity of gas in a closed vessel is halved and the velocities of its molecules are doubled. The final pressure of the gas will be

At what temperature is the r. m. s velocity of a hydrogen molecule equal to that of an oxygen molecule at \[47{}^\circ C\]?

A nitrogen molecule has some rms speed at \[0{}^\circ C\]on the surface of the earth. With this speed, it goes straight up. If there is no collisions with other molecules, the molecule will rise up to a height of

The density of a gas is \[6\times {{10}^{-2}}kg/{{m}^{3}}\] and the root mean square velocity of the gas molecules is 500 m/s. The pressure exerted by the gas on the walls of the vessel is

Figure shows a parabolic graph between T and 1/V for a mixture of a gas undergoing an adiabatic process. What is the ratio of \[{{V}_{rms}}\] of molecules and speed of sound in mixture?

The temperature of an ideal gas is increased from 120 K to 480 K. If at 120 K the root-mean-square velocity of the gas molecules is v, at 480 K it becomes

Why does the pressure of an ideal gas increase when it is heated at constant volume?

Helium gas is filled in a closed vessel (having negligible thermal expansion coefficient) when it is heated from 300 K to 600 K, then average kinetic energy of helium atom will be

The pressure of a gas is raised from \[27{}^\circ C\]to \[927{}^\circ C.\]The root mean square speed is

Consider a gas with density \[\rho \] and \[\overline{c}\] as the root mean square velocity of its molecules contained in a volume. If the system moves as whole with velocity, then the pressure exerted by the gas is

At room temperature a diatomic gas is found to have an r. m. s. speed of \[1930\text{ }m{{s}^{-1}}\]. The gas is:

In kinetic theory of gases, which of the following statement regarding elastic collisions of the molecules is wrong?

The velocity of sound in air is \[332\text{ }m\text{ }{{s}^{-1}}\] at NTP. Find the rms speed of air molecules at NTP. \[\left( \gamma =1.41 \right)\]

A system consists of two stars of equal masses that revolve in a circular orbit about a centre of mass midway between them. Orbital speed of each star is v and period is T. Find the mass M of each star (G is gravitational constant)

Infinite number of masses, each 1 kg are placed along the x-axis \[\operatorname{at} x=\pm 1 m, \pm 2m, \pm 4m, \pm \]\[8m, \pm 16M\ldots \] the magnitude of the resultant gravitational potential in terms of gravitational constant G at the or g in \[(x=0)\] is

The gravitational field due to a mass distribution is \[\operatorname{E}=K/{{x}^{3}}\]in the x-direction. (K is a constant). Taking the gravitational potential to be zero at infinity, its value at a distance x is

The gravitational field in a region is given by\[\vec{g} =5N/kg\hat{i}+12N/kg\hat{j}\]. The change in the gravitational potential energy of a particle of mass 1 kg when it is taken from the origin to a point \[(7m,-3m)\] is: