List of top Physics Questions asked in JEE Advanced

A region in the form of an equilateral triangle (in x-y plane) of height L has a uniform magnetic field 𝐵⃗ pointing in the +z-direction. A conducting loop PQR, in the form of an equilateral triangle of the same height 𝐿, is placed in the x-y plane with its vertex P at x = 0 in the orientation shown in the figure. At 𝑡 = 0, the loop starts entering the region of the magnetic field with a uniform velocity 𝑣 along the +x-direction. The plane of the loop and its orientation remain unchanged throughout its motion.

Which of the following graph best depicts the variation of the induced emf (E) in the loop as a function of the distance (𝑥) starting from 𝑥 = 0?

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 particle of mass 𝑚 is under the influence of the gravitational field of a body of mass 𝑀 (≫ 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 𝑉c(𝑟) = 𝑚𝛼/𝑟 3 , where 𝛼 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 𝑉c(𝑟), but with a new time period \(𝑇_1\), then\( (𝑇_1^2  − 𝑇_0^ 2 )/𝑇_1^ 2\) is given by [𝐺 is the gravitational constant.]

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 𝜃 such that the outgoing ray undergoes minimum deviation in prism \(P_2\). If the respective refractive indices of \(P_1\) and\( P_2\) are \(√ 3 /2\) and \(√3\), then \(\theta  = sin{−1}[\sqrt \frac{ 3}{ 2} sin ( \frac{\pi}{B} )],\) where the value of \(\beta\) is ______.

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 _____

An infinitely long thin wire, having a uniform charge density per unit length of \(5 nC/m,\) is passing through a spherical shell of radius \(1 m\), as shown in the figure. A \(10 nC\) charge is distributed uniformly over the spherical shell. If the configuration of the charges remains static, the magnitude of the potential difference between points P and R, in Volt, is ______. [Given: In SI units \(\frac{1}{ 4πϵ0} = 9 × 10^9 , ln \ 2 = 0.7\). Ignore the area pierced by the wire.]

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

A ball is thrown from the location \((x_0, y_0 ) = (0,0)\) of a horizontal playground with an initial speed \(𝑣_0\) at an angle \(\theta_0\)\(\theta_0\) from the +𝑥-direction. The ball is to be hit by a stone, which is thrown at the same time from the location \((𝑥_1, 𝑦_1 ) = (𝐿, 0).\) The stone is thrown at an angle \((180 − \theta_1 )\) from the +𝑥-direction with a suitable initial speed. For a fixed \(𝑣_0\) , when \((\theta_0 , \theta_1 ) = (45° , 45° ),\) the stone hits the ball after time \(𝑇_1\) , and when \((\theta_0 , \theta_1 ) = (60° , 30° )\), it hits the ball after time \(𝑇_2\) . In such a case,\( (\frac{𝑇1 }{𝑇2} )^2\) is ______.

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

 

A positive, singly ionized atom of mass number \(A_M\) is accelerated from rest by the voltage \(192 V\). Thereafter, it enters a rectangular region of width 𝑤 with magnetic field \(\bar{B_0} = 0.1𝑘̂\)Tesla, as shown in the figure. The ion finally hits a detector at the distance 𝑥 below its starting trajectory. [Given: Mass of neutron/proton =\((5/3) × 10^{−27}\) kg, charge of the electron \(= 1.6 × 10^{−19} C.\)]

Which of the following option(s) is(are) correct?

Two large, identical water tanks, 1 and 2, kept on the top of a building of height H, are filled with water up to height ℎ in each tank. Both the tanks contain an identical hole of small radius on their sides, close to their bottom. A pipe of the same internal radius as that of the hole is connected to tank 2, and the pipe ends at the ground level. When the water flows from the tanks 1 and 2 through the holes, the times taken to empty the tanks are t1 and t2, respectively. If \(H = ( \frac{16}{ 9} ) ℎ\), then the ratio t1/t2 is ___

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

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?

An infinitely long wire, located on the z-axis, carries a current I along the +z-direction and produces the magnetic field \(\bar{B}\) . The magnitude of the line integral \(∫ \overrightarrow{B}.\overrightarrow{dl}\) along a straight line from the point \( (−√3a, a, 0) \)to \((a, a, 0)\) is given by [\(\mu_0\) is the magnetic permeability of free space.]

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 thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). The other end of the string is pivoted to a point O. If a horizontal impulse P is imparted to the rod at a distance x = L/n from the mid-point of the rod (see figure), then the rod and string revolve together around the point O, with the rod remaining aligned with the string. In such a case, the value of n is _____.

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 \(\theta = 30\) , then the electric flux through the curved surface of the cylinder is \(Φ\). If \(\theta= 60\degree\) , then the electric flux through the curved surface becomes \(Φ/√𝑛\), where the value of n is______.

 

The dimensions of a cone are measured using a scale with a least count of 2 mm. The diameter of the base and the height are both measured to be 20.0 cm. The maximum percentage error in thedetermination of the volume is ______.

A spherical soap bubble inside an air chamber at pressure \(𝑃_0 = 10^5 \)Pa has a certain radius so that the excess pressure inside the bubble is Δ𝑃 = 144 Pa. Now, the chamber pressure is reduced to \(8𝑃_0/27\) so that the bubble radius and its excess pressure change. In this process, all the temperatures remain unchanged. Assume air to be an ideal gas and the excess pressure Δ𝑃 in both the cases to be much smaller than the chamber pressure. The new excess pressure Δ𝑃 in Pa is

A source (S) of sound has frequency\( 240 Hz\). When the observer (O) and the source move towards each other at a speed \(v\) with respect to the ground (as shown in Case 1 in the figure), the observer measures the frequency of the sound to be \(288 Hz\). However, when the observer and the source move away from each other at the same speed v with respect to the ground (as shown in Case 2 in the figure), the observer measures the frequency of sound to be \(n\) Hz. 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 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 table tennis ball has radius \((3/2) × 10^{−2} \)m and mass \((22/7) × 10^{−3} \)kg. It is slowly pushed down into a swimming pool to a depth of 𝑑 = 0.7 m below the water surface and then released from rest. It emerges from the water surface at speed 𝑣, without getting wet, and rises up to a height 𝐻. Which of the following option(s) is(are) correct?[Given: \(\pi = 22/7, g = 10 m s ^{−2} \), density of water = \(1 × 10^3 kg\ m^{−3}\) , viscosity of water = \(1 × 10^{−3}\) Pa-s.] 

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?