List of top Physics Questions

The radioactive nuclei \({}^{40}\text{K}\) decay to \({}^{40}\text{Ar}\) with a half-life of \(1.25 \times 10^9\) years. The \({}^{40}\text{K}/{}^{40}\text{Ar}\) isotopic ratio for a particular rock is found to be 50. The age of the rock is \(m \times 10^7\) years. The value of \(m\) is .............. (Round off to 2 decimal places)

Consider a retarder with refractive indices \(n_e = 1.551\) and \(n_o = 1.542\) along the extraordinary and ordinary axes, respectively. The thickness of this retarder for which a left circularly polarized light of wavelength \(600 \, \text{nm}\) will be converted into a right circularly polarized light is ........... µm. (Round off to 2 decimal places).

Water flows in a horizontal pipe in a streamlined manner at an absolute pressure of \(4 \times 10^5 \, \text{Pa}\) and speed of \(6 \, \text{m/s}\). If it exits the pipe at a pressure of \(10^5 \, \text{Pa}\), the speed of water at the exit point is .......... m/s (Round off to 1 decimal place).
(The density of water is \(1000 \, \text{kg/m}^3\))

Consider a thin bi-convex lens of relative refractive index \(n = 1.5\). The radius of curvature of one surface of the lens is twice that of the other. The magnitude of larger radius of curvature in units of the focal length of the lens is ............. (Round off to 1 decimal place).

One mole of an ideal gas having specific heat ratio (\(\gamma\)) of 1.6 is mixed with one mole of another ideal gas having specific heat ratio of 1.4. If \(C_V\) and \(C_P\) are the molar specific heat capacities of the gas mixture at constant volume and pressure, respectively, which of the following is/are correct? (\(R\) denotes the universal gas constant.)

A spherical dielectric shell with inner radius \(a\) and outer radius \(b\), has polarization \(\vec{P} = \dfrac{k}{r^2}\hat{r}\), where \(k\) is a constant and \(\hat{r}\) is the unit vector along the radial direction. Which of the following statements is/are correct?

For electric and magnetic fields, \(\vec{E}\) and \(\vec{B}\), due to a charge density \(\rho(\vec{r},t)\) and a current density \(\vec{J}(\vec{r},t)\), which of the following relations is/are always correct?

An object executes simple harmonic motion along the x-direction with angular frequency \(\omega\) and amplitude \(a\). The speed of the object is 4 cm/s and 2 cm/s when it is at distances 2 cm and 6 cm, respectively, from the equilibrium position. Which of the following is/are correct?

A thin rod of uniform density and length \(2\sqrt{3}\, \text{m}\) is undergoing small oscillations about a pivot point. The time period of oscillation (\(T_m\)) is minimum when the distance of the pivot point from the center-of-mass of the rod is \(x_m\). Which of the following is/are correct? (Assume acceleration due to gravity \(g = 10\, \text{m/s}^2\))

Consider a vector function \(\vec{u}(\vec{r})\) and two scalar functions \(\psi(\vec{r})\) and \(\phi(\vec{r})\). The unit vector \(\hat{n}\) is normal to the elementary surface \(dS\), \(dV\) is an infinitesimal volume, \(d\vec{l}\) is an infinitesimal line element, and \(\partial / \partial n\) denotes the partial derivative along \(\hat{n}\). Which of the following identities is/are correct?

In the circuit shown in the figure, both OPAMPs are ideal. The output for the circuit \(V_{out}\) is:

For an unbiased Silicon \(n\text{-}p\text{-}n\) transistor in thermal equilibrium, which one of the following electronic energy band diagrams is correct? (\(E_c\) = conduction band minimum, \(E_v\) = valence band maximum, \(E_F\) = Fermi level.)

Consider a one-dimensional infinite potential well of width \(a\). This system contains five non-interacting electrons, each of mass \(m\), at temperature \(T = 0 \, K\). The energy of the highest occupied state is:

A linear operator \(\hat{O}\) acts on two orthonormal states of a system \(\psi_1\) and \(\psi_2\) as per the following: \[ \hat{O}\psi_1 = \psi_2, \hat{O}\psi_2 = \frac{1}{\sqrt{2}}(\psi_1 + \psi_2) \] The system is in a superposed state defined by \[ \psi = \frac{1}{\sqrt{2}}\psi_1 + \frac{i}{\sqrt{2}}\psi_2 \] The expectation value of \(\hat{O}\) in the state \(\psi\) is:

A thin conducting square loop of side \(L\) is placed in the first quadrant of the \(xy\)-plane with one of the vertices at the origin. If a changing magnetic field \(\vec{B}(t) = B_0(52yt\,\hat{x} + xzt\,\hat{y} + 3y^2t^2\,\hat{z})\) is applied, where \(B_0\) is a constant, then the magnitude of the induced electromotive force in the loop is:

Consider the motion of a quantum particle of mass \(m\) and energy \(E\) under the influence of a step potential of height \(V_0\). If \(R\) denotes the reflection coefficient, which one of the following statements is true?

The figure below shows a cubic unit cell with lattice constant \(a\). The shaded crystallographic plane intersects the x-axis at 0.5a. The Miller indices of the shaded plane are:

Two stationary point particles with equal and opposite charges are at some fixed distance from each other. The points having zero electric potential lie on:

One point charge (q) each, is placed along a line at 3 different points \(x = 0\), \(x = 2 \, \text{nm}\) and \(x = 6 \, \text{nm}\). The force between two charges separated by 2 nm is 2 piconewton (pN). The magnitude of force (in pN) on the charge in the middle due to the other two charges is ..............

Consider two bodies with equal masses of \( 10^{12} \) kg each and R distance apart. Let G be the gravitational constant and \( V_0 \) be a constant with dimensions of energy. Which of the following represent(s) gravitational potential energy (V) between the bodies, such that Newton's law of gravitation is valid?

Which of the following is(are) CORRECT?

Consider monoatomic ideal gas molecules of equal mass \( m \) in thermal equilibrium, at temperature \( T \). Which one of the following equations is correct? (the angular brackets denote average, \( k_B \) is Boltzmann constant, \( v \) is velocity, and \( v_x \) is the x-component of velocity)

An ideal gas undergoes an isothermal expansion along path AB, adiabatic expansion along BC, isobaric compression along CD, isothermal compression along DE, and adiabatic compression along EA, as shown in the figure. The work done by the gas along the process BC is 10 J. The change in the internal energy along process EA is 16 J. The absolute value of the change in the internal energy along the process CD is ............ J.

Using a battery, a 10 pF capacitor is charged to 50 V and then the battery is removed. After that, a second uncharged capacitor is connected to the first capacitor in parallel. If the final voltage across the second capacitor is 20 V, its capacitance is .............. pF.

The line integral of the vector function \(u(x, y) = 2y \, \hat{i} + x \, \hat{j}\) along the straight line from (0, 0) to (2, 4) is ..........