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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:
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):
A certain number of spherical drops of a liquid of radius $r$ coalesce to form a single drop of radius $R$ and volume $V$. If $T$ is the surface tension of the liquid, then:
The amount of heat energy required to raise the temperature of 1 g of Helium at NTP, from $T_1$ K to $T_2$ K is:
A bar magnet of length $l$ and magnetic dipole moment $M$ is bent in the form of an arc as shown in the figure. The new magnetic dipole moment will be:
Wavelength of ray of light is 0.00006 m. It is equal to:
An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in the equilibrium state. The energy required to rotate it by $60^\circ$ is $W$. Now the torque required to keep the magnet in this new position is:
A particle of mass $m$ is projected with velocity $v$ making an angle of $45^\circ$ with the horizontal. When the particle lands on level ground, the magnitude of change in its momentum will be:
Given below are two statements: Assertion (A): The stretching of a spring is determined by the shear modulus of the material of the spring. Reason (R): A coil spring of copper has more tensile strength than a steel spring of the same dimensions.
A soap bubble, having a radius of $1 \text{ mm}$, is blown from a detergent solution having a surface tension of $2.5 \times 10^{-2} \text{ N/m}$. The pressure inside the bubble equals the pressure at a point $Z_0$ below the free surface of the water in a container. Taking $g = 10 \text{ m/s}^2$ and the density of water $\rho = 10^3 \text{ kg/m}^3$, the value of $Z_0$ is: