Question Bank Directory

A 250-turn rectangular coil with a length of $2.1 \text{ cm}$ and a width of $1.25 \text{ cm}$ carries a current of $85 \text{ }\mu\text{A}$ and is subjected to a magnetic field of strength $0.85 \text{ T}$. What is the work done to rotate the coil by $180^\circ$ against the torque?

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)

A bar magnet of length L and magnetic dipole moment M is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be:

Which of the following is correct about viroids?

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:

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:

Zr ($Z = 40$) and Hf ($Z = 72$) have similar atomic and ionic radii because of: