List of top Physics Questions

Consider a slowly charging parallel plate capacitor (distance between the plates is d) having circular plates each with an area A, as shown in the figure below. An electric field of magnitude $E = E_0\sin(\omega t)$ exists between the plates while charging. The associated magnitude of the magnetic field B at the periphery (outer edge) of the capacitor is
(Neglect fringe effects)

For an electromagnetic wave, consider an electric field $E = E_0e^{-i[a(x+y)-\omega t]\hat{k}$. The corresponding magnetic field $B$ is ($E_0, a, \omega$ are constants of appropriate dimensions and c is the speed of light)}

An unpolarized light ray passing through air (refractive index $n_a = 1$) is incident on a glass slab (refractive index $n_g = \sqrt{3}$) at an angle of 60°, as shown in the figure below. The amplitude of the in-plane (x-y) electric field component of the incident light is 4 V/m and amplitude of the out of plane (z) electric field component is 3 V/m. After passing through the glass slab, the electric field amplitude (in V/m) of the light is

Two masses, $M_1$ and $M_2$, are connected through a massless spring of spring constant k, as shown in the figure below. The mass $M_1$ is at rest against a rigid wall. Both $M_1$ and $M_2$ are on a frictionless surface. The mass $M_2$ is pushed towards $M_1$ by a distance x from its equilibrium position and then released. After $M_1$ leaves the wall, the speed of the center of mass of the composite system is

Three particles of equal mass M, interacting via gravity, lie on the vertices of an equilateral triangle of side d, as shown in the figure below. The whole system is rotating with an angular velocity $\omega$ about an axis perpendicular to the plane of the system and passing through the center of mass. The value of $\omega$, for which the distance between the masses remains d, is
(G is the universal gravitational constant)

In the circuit given below, the frequency of the input voltage $V_{IN}$ is $\omega = 10^4$ rad/s. The output voltage $V_{AB}$ leads $V_{IN}$ by

Consider radioactive decays $A \to B$ with half-life $(T_{1/2})_A$, and $B \to C$ with half-life $(T_{1/2})_B$. At any time t, the number of nuclides of B is given by
$ (N_B)_t = \frac{\lambda_A{\lambda_B - \lambda_A}(N_A)_0 (e^{-\lambda_A t} - e^{-\lambda_B t}) $,
where $(N_A)_0$ is the number of nuclides of A at $t = 0$. The decay constants of A and B are $\lambda_A$ and $\lambda_B$, respectively.
If $(T_{1/2})_B<(T_{1/2})_A$, then the ratio $\frac{(N_B)_t}{(N_A)_t}$ at time $t \gg (T_{1/2})_A$ is}
$(N_A)_t$ is the number of nuclides of A at time t

A charge q is placed at the centre of the base of a square pyramid. The net outward electric flux across each of the slanted faces is
(Consider permittivity as $\epsilon_0$)

Consider a metal sphere enclosed concentrically within a spherical shell. The inner sphere of radius a carries charge Q. The outer shell of radius 2a also has charge Q. The variation of the magnitude E of the electric field as a function of distance r from the center O is

If the input voltage waveform $V_{IN}$ is a ramp function (as shown in the $V_{IN} - t$ plot below), then the output wave form ($V_{OUT}$) for the given circuit diagram having an ideal operational amplifier (Op-Amp) is

For a non-relativistic free particle, the ratio of phase velocity to group velocity is

Consider a parallel plate capacitor (distance between the plates d, and permittivity $\epsilon_0$) as shown in the figure below. The space charge density between the plates varies as $\rho(x) = \rho_0 e^{-x$. Voltage $V = 0$ both at $x = 0$ and $x = d$. The voltage $V(x)$ at point P between the plates is}

$\rho_0$ is a constant of appropriate dimensions

Two parallel light rays 1 and 2 are incident from air on a system consisting of media P, Q, and air, as shown in the figure below. The incident angle is 45°. Ray 1 passes through medium P, air and medium Q and ray passes through media P and Q before leaving the system. After passing through the system, the angular deviation (in radians) between the two rays is

The dimensions of the media and their refractive indices ($n_a, n_P$ and $n_Q$) are shown in the figure

A current carrying circular loop of area $ A $ produces a magnetic field $ B $ at its centre. Show that the magnetic moment of the loop is: \[ \mu = \frac{2BA}{\mu_0} \sqrt{\frac{A}{\pi}} \]

In the circuit shown, the charge on the left plate of the 20 µF capacitor is $ -50\,\mu C $. The charge on the right plate of the 12 µF capacitor is:

You are required to design an air-filled solenoid of inductance 0.016 H having a length 0.81 m and radius 0.02 m. The number of turns in the solenoid should be:

A ball is projected vertically up with speed $ V_0 $ from a certain height $ H $. When the ball reaches the ground, the speed is $ 3V_0 $. The time taken by the ball to reach the ground and height $ H $ respectively are:

A current-carrying coil is placed in an external uniform magnetic field. The coil is free to turn in the magnetic field. What is the net force acting on the coil? Obtain the orientation of the coil in stable equilibrium. Show that in this orientation the flux of the total field (field produced by the loop + external field) through the coil is maximum.

Potential energy is not defined for which of the following forces?

A conductor of length $ l $ is connected across an ideal cell of emf $ E $. Keeping the cell connected, the length of the conductor is increased to $ 2l $ by gradually stretching it. If $ R $ and $ R' $ are the initial and final values of resistance, and $ v_d $ and $ v'_d $ are the initial and final values of drift velocity, find the relation between (i) $ R' $ and $ R $ and (ii) $ v'_d $ and $ v_d $.

A disc of mass $ M $ and radius $ R $ is rolling without slipping with linear velocity $ v $. What is its total kinetic energy?

A wheel of mass $ 4M $ and radius $ R $ is made of a thin uniform distribution of mass $ 3M $ at the rim and a point mass $ M $ at the center. The spokes of the wheel are massless. The center of mass of the wheel is connected to a horizontal massless rod of length $ 2R $, with one end fixed at $ O $, as shown in the figure. The wheel rolls without slipping on horizontal ground with angular speed $ \Omega $. If $ \vec{L} $ is the total angular momentum of the wheel about $ O $, then the magnitude $ \left| \frac{d\vec{L}}{dt} \right| = N(MR^2 \Omega^2) $. The value of $ N $ (in integer) is:

Explain the following observations using Einstein’s photoelectric equation:
(a) Photoelectric emission does not occur from a surface when the frequency of the light incident on it is less than a certain minimum value.
(b) It is the frequency, and not the intensity of the incident light which affects the maximum kinetic energy of the photoelectrons.
(c) The cut-off voltage $ V_0 $ versus frequency $ \nu $ of the incident light curve is a straight line with a slope $ \frac{h}{e} $.

Mention the most important conclusion of Rutherford's alpha-particle scattering experiment. Define isotopic, isobaric, and isotonic nuclei. Find the energy equivalent to one atomic mass unit in joules and MeV (1 u = 1.6605 × $10^{-27}$ kg).

Explain the difference between self-inductance and mutual inductance. Define the coefficient of self-inductance and coefficient of mutual inductance. A plane coil of area 100 cm$^2$ is rotating in a magnetic field of 2 weber/m$^2$ with angular velocity 20 rad/s. What will be the maximum induced electromotive force in the coil?