List of top Physics Questions asked in JEE Advanced

A point source \(S\) emits unpolarized light uniformly in all directions. At two points A and B, the ratio \(r = I_A/I_B\) of the intensities of light is \(2\). If a set of two polaroids having 45° angle between their pass-axes is placed just before point B, then the new value of r will be ____

A disc of mass \(M\) and radius \(R\) is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its circumference. Another disc of the same mass \(M\) and radius \(R/2\) is fixed to the motor’s thin shaft. Initially, both the discs are at rest. The motor is switched on so that the smaller disc rotates at a uniform angular speed \(\omega\). If the angular speed at which the large disc rotates is \(\omega/n\), then the value of \(n\) is _____

The specific heat capacity of a substance is temperature dependent and is given by the formula C = kT, where k is a constant of suitable dimensions in SI units, and T is the absolute temperature. If the heat required to raise the temperature of 1 kg of the substance from −73 ° C to 27 ° C is nk, the value of n is ___[Given: 0 K = −273 °C.]

A glass beaker has a solid, plano-convex base of refractive index 1.60, as shown in the figure. The radius of curvature of the convex surface (SPU) is 9 cm, while the planar surface (STU) acts as a mirror. This beaker is filled with a liquid of refractive index n up to the level QPR. If the image of a point object O at a height of ℎ (OT in the figure) is formed onto itself, then, which of the following option(s) is(are) correct?

Two uniform strings of mass per unit length \(\mu\) and \(4\mu\), and length \(L\) and \(2L\), respectively, are joined at point \(O\), and tied at two fixed ends \(P\) and \(Q\), as shown in the figure. The strings are under a uniform tension \(T\). If we define the frequency \(v_0 = \frac{1}{2L} \sqrt{\frac{T}{\mu}}\), which of the following statements is(are) correct?

A particle of mass m is moving in a circular orbit under the influence of the central force\( f(r) = −kr\), corresponding to the potential energy \(v(r) = \frac{kr^2}{2}\), where \(k\) is a positive force constant and \( r\) is the radial distance from the origin. According to the Bohr’s quantization rule, the angular momentum of the particle is given by \(L= nℏ\), where\( ℏ = ℎ/(2pi), ℎ\) is the Planck’s constant, and \(n\) a positive integer. If \(v\) and \(E\) are the speed and total energy of the particle, respectively, then which of the following expression(s) is(are) correct?

A block of mass \(5 kg\) moves along the \(x-\)direction subject to the force \(F = (−20x + 10) N,\) with the value of  \(x \) in metre. At time \(t = 0 s,\) it is at rest at position \(x = 1 m\). The position and momentum of the block at \(t = (\pi/4)\) s are

Two beads, each with charge q and mass m, are on a horizontal, frictionless, non-conducting, circular hoop of radius R. One of the beads is glued to the hoop at some point, while the other one performs small oscillations about its equilibrium position along the hoop. The square of the angular frequency of the small oscillations is given by [ \(\epsilon_0 \)is the permittivity of free space.]

A dimensionless quantity is constructed in terms of electronic charge \(e\), permittivity of free space \(\epsilon_0\) , Planck’s constant ℎ, and speed of light c. If the dimensionless quantity is written as \(e^\alpha\epsilon_0^\beta h^\gamma c^\delta\)and n is a non-zero integer, then\((\alpha, \beta,\gamma,\delta)\) is given by

If the collision occurs at time \( t_0 = \frac{\pi}{2\omega} \), then the value of \( \frac{4b^2}{a^2} \) will be:

Two equilateral-triangular prisms \(P_1\) and \(P_2\) are kept with their sides parallel to each other, in vacuum, as shown in the figure. A light ray enters prism \(P_1\) at an angle of incidence \(\theta\) such that the outgoing ray undergoes minimum deviation in prism \(P_2\). If the respective refractive indices of \(P_1\) and \(P_2\) are \(\sqrt{3}/\sqrt{2})\) and \(\sqrt{3}\), then \(\theta = \sin^{-1}\left(\sqrt{3}/\sqrt{2}) \sin\left(\frac{\pi}{\beta}\right)\right)\), where the value of \(\beta\) is \_\_\_\_.
\includegraphics[width=0.5\linewidth]{p11.png}

A charge is kept at the central point \( P \) of a cylindrical region. The two edges subtend a half-angle \(\theta\) at \( P \), as shown in the figure. When \(\theta = 30^\circ\), then the electric flux through the curved surface of the cylinder is \(\Phi\). If \(\theta = 60^\circ\), then the electric flux through the curved surface becomes \(\frac{\Phi}{\sqrt{n}}\), where the value of \(n\) is \_\_\_\_. \includegraphics[width=0.3\linewidth]{ph8.png}

A small electric dipole \( \vec{p}_0 \), having a moment of inertia \( I \) about its center, is kept at a distance \( r \) from the center of a spherical shell of radius \( R \). The surface charge density \( \sigma \) is uniformly distributed on the spherical shell. The dipole is initially oriented at a small angle \( \theta \) as shown in the figure. While staying at a distance \( r \), the dipole is free to rotate about its center. If released from rest, then which of the following statement(s) is(are) correct? \[ \epsilon_0 \text{ is the permittivity of free space.} \]
\includegraphics[width=0.4\linewidth]{ph5.png}

A particle of mass \( m \) is under the influence of the gravitational field of a body of mass \( M \) (\( M \gg m \)). The particle is moving in a circular orbit of radius \( r_0 \) with time period \( T_0 \) around the mass \( M \). Then, the particle is subjected to an additional central force, corresponding to the potential energy \( V(r) = \frac{\alpha m{r^3} \), where \( \alpha \) is a positive constant of suitable dimensions and r is the distance from the center of the orbit. If the particle moves in the same circular orbit of radius \(r_0\) in the combined gravitational potential due to M and \(V_c(r)\), but with a new time period \(T_1\), then } \[ \frac{T_1^2 - T_0^2}{T_1^2} \] is given by: [G is the gravitational constant]

A thin stiff insulated metal wire is bent into a circular loop with its two ends extending tangentially from the same point of the loop. The wire loop has mass 𝑚 and radius 𝑟 and it is in a uniform vertical magnetic field \(B_0\), as shown in the figure. Initially, it hangs vertically downwards, because of acceleration due to gravity 𝑔, on two conducting supports at P and Q. When a current 𝐼 is passed through the loop, the loop turns about the line PQ by an angle 𝜃 given by

 

In a Young’s double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of 0.8 mm. The distance between the slits at time t is given by 𝑑 = (0.8 + 0.04 sin 𝜔𝑡) mm, where 𝜔 = 0.08 rad s −1 . The distance of the screen from the slits is 1 m and the wavelength of the light used to illuminate the slits is 6000 Å. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point O.

Two particles, 1 and 2, each of mass 𝑚, are connected by a massless spring, and are on a horizontal frictionless plane, as shown in the figure. Initially, the two particles, with their center of mass at \(𝑥_0\), are oscillating with amplitude 𝑎 and angular frequency 𝜔. Thus, their positions at time 𝑡 are given by \(x_1 (t) = (x_0 + d) + \alpha \  sin \omega t\) and \(x_2t = (x_0 -d) − \alpha sin \ wt,\) respectively, where \(𝑑 > 2𝑎.\) Particle 3 of mass 𝑚 moves towards this system with speed 𝑢0 = 𝑎𝜔/2, and undergoes instantaneous elastic collision with particle 2, at time \(𝑡_0\). Finally, particles 1 and 2 acquire a center of mass speed \(𝑣_{cm}\) and oscillate with amplitude 𝑏 and the same angular frequency 𝜔.

A monochromatic light wave is incident normally on a glass slab of thickness as shown in the figure. The refractive index of the slab increases linearly from n₁ to n₂ over the height of h. Which of the following statements is/are true about the light wave emerging out of the slab?

Monochromatic light wave