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If $C_p$ and $C_v$ denote the specific heats (per unit mass) of an ideal gas of molecular weight $M$, then:
A given sample of an ideal gas occupies a volume $V$ at a pressure $p$ and absolute temperature $T$. The mass of each molecule of the gas is $m$. Which of the following gives the density of the gas?
Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:
Electromagnets are made of soft iron because soft iron has:
For a gas, $R/C_V = 0.67$. This gas is made up of molecules which are:
A gas mixture consists of 2 moles of $O_2$ and 4 moles of Ar at temperature T. Neglecting all vibrational modes, the total internal energy of the system is:
Dependence of intensity of gravitational field (E) of earth with distance (r) from centre of earth is correctly represented by:
A particle of mass M is situated at the centre of a spherical shell of mass M and radius a. The gravitational potential at a point situated at a/2 distance from the centre will be:
The average thermal energy for a mono-atomic gas is: ($k_B$ is Boltzmann constant and $T$ absolute temperature)
Kepler's third law states that the square of the period of revolution (T) of a planet around the sun, is proportional to the third power of the average distance r between the sun and planet i.e. $T^2 = Kr^3$, here K is constant. If the masses of the sun and planet are M and m respectively, then as per Newton's law of gravitation, the force of attraction between them is $F = GMm/r^2$, here G is gravitational constant. The relation between G and K is described as:
A spherical ball is dropped into a long column of a highly viscous liquid. The graph that represents the speed of the ball ($v$) as a function of time ($t$) is:
A sheet is placed on a horizontal surface in front of a strong magnetic pole. A force is needed to: (A) hold the sheet there if it is magnetic. (B) hold the sheet there if it is non-magnetic. (C) move the sheet away from the pole with uniform velocity if it is conducting. (D) move the sheet away from the pole with uniform velocity if it is both, non-conducting and non-polar. Choose the correct statement(s) from the options given below:
A cylinder contains hydrogen gas at a pressure of $249 \text{ kPa}$ and temperature $27^\circ\text{C}$. Its density is: ($R=8.3 \text{ J mol}^{-1}\text{K}^{-1}$)
The mean free path of molecules of a gas (radius $r$) is inversely proportional to:
Match Column-I and Column-II and choose the correct match from the given choices. **Column-I** (P) Root mean square speed of gas molecules (Q) The pressure exerted by an ideal gas (R) The average kinetic energy of a molecule (S) The total internal energy of a mole of a diatomic gas **Column-II** (1) $\frac{1}{3}nm\bar{v}^2$ (2) $\sqrt{\frac{3RT}{M}}$ (3) $\frac{5}{2}RT$ (4) $\frac{3}{2}k_BT$
The molecules of a given mass of gas have rms velocity of $200 \text{ m s}^{-1}$ at $27^{\circ}\text{C}$ and $1.0 \times 10^5 \text{ N m}^{-2}$ pressure. When the temperature and pressure of the gas are increased to, respectively, $127^{\circ}\text{C}$ and $0.05 \times 10^5 \text{ N m}^{-2}$, the rms velocity of its molecules in $\text{m s}^{-1}$ will become:
Two identical bar magnets are fixed with their centres at a distance $d$ apart. A stationary charge $Q$ is placed at $P$ in between the gap of the two magnets at a distance $D$ from the centre $O$ as shown in the figure. The force on the charge $Q$ is:
The mean free path for a gas, with molecular diameter $d$ and number density $n$, can be expressed as:
At $10^\circ\text{C}$ the value of the density of a fixed mass of an ideal gas divided by its pressure is $x$. At $110^\circ\text{C}$ this ratio is:
A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when: