List of practice Questions

The electrostatic energy (in units of \( \frac{1}{4\pi \epsilon_0} \, \text{J} \)) of a uniformly charged spherical shell of total charge 5 C and radius 4 m is ...........

An infinitely long very thin straight wire carries uniform line charge density \( 8\pi \times 10^{-2} \, \text{C/m} \). The magnitude of electric displacement vector at a point located 20 mm away from the axis of the wire is ......... C/m².

An atomic nucleus X with half-life \( T_X \) decays to a nucleus Y, which has half-life \( T_Y \). The condition(s) for secular equilibrium is/are

In a typical human body, the amount of radioactive \(^{40}K\) is \(3.24 \times 10^{-5}\) percent of its mass. The activity due to \(^{40}K\) in a human body of mass 70 kg is .................. kBq.

Sodium (Na) exhibits body-centered-cubic (BCC) crystal structure with atomic radius 0.186 nm. The lattice parameter of Na unit cell is ................... nm.

Light of wavelength 680 nm is incident normally on a diffraction grating having 4000 lines/cm. The diffraction angle (in degrees) corresponding to the third-order maximum is ........

Two gases having molecular diameters \( D_1 \) and \( D_2 \), and mean free paths \( \lambda_1 \) and \( \lambda_2 \), respectively, are trapped separately in identical containers. If \( D_2 = 2D_1 \), then \( \lambda_1 / \lambda_2 = \) ..........

Which of the following statement(s) is/are true?

For an underdamped harmonic oscillator with velocity \( v(t) \),

Out of the following statements, choose the correct option(s) about a perfect conductor.

In the X-ray diffraction pattern recorded for a simple cubic solid (lattice parameter \( a = 1 \) Å) using X rays of wavelength 1 Å, the first order diffraction peak(s) would appear for the

Consider a classical particle subjected to an attractive inverse-square force field. The total energy of the particle is \( E \) and the eccentricity is \( \epsilon \). The particle will follow a parabolic orbit if

The relation between the nuclear radius \( R \) and the mass number \( A \), given by \( R = 1.2 A^{1/3} \) fm, implies that

Consider an object moving with a velocity \( \vec{v} \) in a frame which rotates with a constant angular velocity \( \vec{\omega} \). The Coriolis force experienced by the object is

The gradient of a scalar field \( S(x, y, z) \) has the following characteristic(s).

A thermodynamic system is described by the \( P, V, T \) coordinates. Choose the valid expression(s) for the system.

The maximum number of intensity minima that can be observed in the Fraunhofer diffraction pattern of a single slit (width 10 µm) illuminated by a laser beam (wavelength 0.630 µm) will be

Which one of the following is an impossible magnetic field \(\vec{B}\)?

If the motion of a particle is described by \( x = 5 \cos(8\pi t), y = 5 \sin(8\pi t) \) and \( z = 5t \), then the trajectory of the particle is

A $\gamma$-ray photon emitted from a $^{137}$Cs source collides with an electron at rest. If the Compton shift of the photon is $3.25 \times 10^{-13}$ m, then the scattering angle is closest to (Planck’s constant $h = 6.626 \times 10^{-34}$ J s, electron mass $m_e = 9.109 \times 10^{-31}$ kg and velocity of light in free space $c = 3 \times 10^8$ m/s)

During free expansion of an ideal gas under adiabatic condition, the internal energy of the gas

Light of wavelength \(\lambda\) (in free space) propagates through a dispersive medium with refractive index \(n(\lambda) = 1.5 + 0.6\lambda\). The group velocity of a wave traveling inside this medium in units of \(10^8\) m/s is

A red star having radius \( r_R \) at a temperature \( T_R \) and a white star having radius \( r_W \) at a temperature \( T_W \), radiate the same total power. If these stars radiate as perfect black bodies, then

The mass per unit length of a rod (length 2 m) varies as \( \rho = 3 \, \text{kg/m} \). The moment of inertia (in kg m\(^2\)) of the rod about a perpendicular-axis passing through the tip of the rod (at \( x = 0 \)) is

The amount of work done to increase the speed of an electron from \( v = c/3 \) to \( v = 2c/3 \) is \[ c = 3 \times 10^8 \, \text{m/s}, \text{ rest mass of electron is } 0.511 \, \text{MeV} \]