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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:
Starting from the centre of the earth, having radius R, the variation of g (acceleration due to gravity) is shown by:
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:
In the given V-T diagram, what is the relation between pressure $P_1$ and $P_2$?
A cylinder contains hydrogen gas at a pressure of $249 \text{ kPa}$ and temperature $27^\circ\text{C}$. Its density is: ($R=8.3 \text{ J mol}^{-1}\text{K}^{-1}$)
One mole of an ideal monatomic gas undergoes a process described by the equation $PV^3 = \text{constant}$. The heat capacity of the gas during this process is:
The mean free path of molecules of a gas (radius $r$) is inversely proportional to:
A short bar magnet of magnetic moment $0.4 \text{ J T}^{-1}$ is placed in a uniform magnetic field of $0.16 \text{ T}$. The magnet is in stable equilibrium when the potential energy is:
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 temperature of a gas is $-50^\circ\text{C}$. To what temperature the gas should be heated so that the RMS speed is increased by 3 times?
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:
The volume occupied by the molecules contained in $4.5 \text{ kg}$ water at STP, if the molecular forces vanish away, is:
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:
The following figures show the arrangement of bar magnets in different configurations. Each magnet has a magnetic dipole moment. Which configuration has the highest net magnetic dipole moment?
A mass m is attached to a thin wire and whirled in a vertical circle. The wire is most likely to break when:
A monoatomic gas at a pressure $p$, having a volume $V$ expands isothermally to a volume $2V$ and then adiabatically to a volume $16V$. The final pressure of the gas is: (take $\gamma = 5/3$)
The amount of energy required to form a soap bubble of radius $2 \text{ cm}$ from a soap solution is nearly: (Given: surface tension of soap solution $= 0.03 \text{ N m}^{-1}$)
A body of mass $6 \text{ kg}$ is moving from its initial position $A$ to the next position $B$ as shown in the figure. From $A$ to $B$, the value of the momentum of the body is (in SI units):