List of top Physics Questions asked in JEE Advanced

One end of a horizontal uniform beam of weight $W$ and length $L$ is hinged on a vertical wall at point $O$ and its other end is supported by a light inextensible rope. The other end of the rope is fixed at point $Q$, at a height $L$ above the hinge at point $O$ a block of weight $\alpha W$ is attached at the point $P$ of the beam, as shown in the figure (not to scale). The rope can sustain a maximum tension of $(2 \sqrt{2})$ W. Which of the following statement(s) is(are) correct?

A thin rod of mass $M$ and length $a$ is free to rotate in horizontal plane about a fixed vertical axis passing through point $O$. A thin circular disc of mass $M$ and of radius $a / 4$ is pivoted on this rod with its center at a distance $a / 4$ from the free end so that it can rotate freely about its vertical axis, as shown in the figure. Assume that both the rod and the disc have uniform density and they remain horizontal during the motion. An outside stationary observer finds the rod rotating with an angular velocity $\Omega$ and the disc rotating about its vertical axis with angular velocity $4\, \Omega$. The total angular momentum of the system about the point $O$ is $\left(\frac{ Ma ^{2} \Omega}{48}\right) n$. The value of $n$ is ______

A thin rod of mass M and length 𝑎 is free to rotate in horizontal plane about a fixed vertical axis passing through point O

A soft plastic bottle, filled with water of density 1 gm/cc, carries an inverted glass test tube with some air (ideal gas) trapped as shown in the figure. The test tube has a mass of 5 gm, and it is made of a thick glass of density 2.5 gm/cc. Initially, the bottle is sealed at atmospheric pressure p₀ = 10⁵Pa so that the volume of the trapped air is V₀ = 3.3 cc. When the bottle is squeezed from outside at a constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure p₀ + Δp without changing its orientation. At this pressure, the volume of the trapped air is V₀ – ΔV.
Let ΔV = X cc and Δp = Y × 10³ Pa.

In the circuit, a metal filament lamp is connected in series with a capacitor of capacitance $C\, \mu F$ across a $200\, V , 50\, Hz$ supply The power consumed by the lamp is $500\, W$ while the voltage drop across it is $100\, V$ Assume that there is no inductive load in the circuit Take $r m s$ values of the voltages The magnitude of the phase-angle (in degrees) between the current and supply voltage is $\phi $ Assume, $\pi \sqrt{3} \approx 5$ The value of $\phi$ is _____

A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} \,m / s$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $05\, s$ after the splitting. The other part, $t$ seconds after the splitting, falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g =10 \,m / s ^{2}$.
The value of $x$ is ______

A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C _{ V }=2 R$ Here, $R$ is the gas constant Initially, each side has a volume $V _{0}$ and temperature $T_{0}$ The left side has an electric heater, which is turned on at very low power to transfer heat $Q$ to the gas on the left side As a result the partition moves slowly towards the right reducing the right side volume to $V _{0} / 2$ Consequently, the gas temperatures on the left and the right sides become $T _{ L }$ and $T _{ R }$, respectively Ignore the changes in the temperatures of the cylinder, heater and the partition The value of $\frac{ T _{ R }}{ T _{0}}$ is

A thermally insulating cylinder has a thermally insulating and frictionless movable partition in the middle, as shown in the figure below. On each side of the partition, there is one mole of an ideal gas, with specific heat at constant volume, $C _{ V }=2 R$. Here, $R$ is the gas constant Initially, each side has a volume $V _{0}$ and temperature $T_{0}$ The left side has an electric heater, which is turned on at very low power to transfer heat $Q$ to the gas on the left side. As a result the partition moves slowly towards the right reducing the right side volume to $\frac{V _{0} }{ 2}$. Consequently, the gas temperatures on the left and the right sides become $T _{ L }$ and $T _{ R }$, respectively. Ignore the changes in the temperatures of the cylinder, heater and the partition

A special metal S conducts electricity without any resistance A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux The induced current in the loop cannot decay due to its zero resistance This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux Consider such a loop, of radius a, with its centre at the origin A magnetic dipole of moment $m$ is brought along the axis of this loop from infinity to a point at distance $r(>>$ a) from the centre of the loop with its north pole always facing the loop, as shown in the figure below The magnitude of magnetic field of a dipole $m$, at a point on its axis at distance $r$, is $\frac{\mu_{0}}{2 \pi} \frac{ m }{ r ^{3}}$, where $\mu_{0}$ is the permeability of free space The magnitude of the force between two magnetic dipoles with moments, $m _{1}$ and $m _{2}$, separated by a distance $r$ on the common axis, with their north poles facing each other, is $\frac{ km _{1} m _{2}}{ r ^{4}}$, where $k$ is a constant of appropriate dimensions The direction of this force is along the line joining the two dipoles When the dipole $m$ is placed at a distance $r$ from the center of the loop (as shown in the figure), the current induced in the loop will be proportional to

A special metal S conducts electricity without any resistance. A closed wire loop, made of S, does not allow any change in flux through itself by inducing a suitable current to generate a compensating flux. The induced current in the loop cannot decay due to its zero resistance. This current gives rise to a magnetic moment which in turn repels the source of magnetic field or flux. Consider such a loop, of radius a, with its centre at the origin. A magnetic dipole of moment $m$ is brought along the axis of this loop from infinity to a point at distance $r(>>$ a) from the centre of the loop with its north pole always facing the loop, as shown in the figure below.
The magnitude of magnetic field of a dipole $m$, at a point on its axis at distance $r$, is $\frac{\mu_{0}}{2 \pi} \frac{ m }{ r ^{3}}$, where $\mu_{0}$ is the permeability of free space. The magnitude of the force between two magnetic dipoles with moments, $m _{1}$ and $m _{2}$, separated by a distance $r$ on the common axis, with their north poles facing each other, is $\frac{ km _{1} m _{2}}{ r ^{4}}$, where $k$ is a constant of appropriate dimensions. The direction of this force is along the line joining the two dipoles.

In the circuit, a metal filament lamp is connected in series with a capacitor of capacitance $C\, \mu F$ across a $200\, V , 50\, Hz$ supply. The power consumed by the lamp is $500\, W$ while the voltage drop across it is $100\, V$. Assume that there is no inductive load in the circuit. Take $r m s$ values of the voltages. The magnitude of the phase-angle (in degrees) between the current and supply voltage is $\phi $. Assume, $\pi \sqrt{3} \approx 5$

In the circuit, a metal filament lamp is connected in series with a capacitor of capacitance $C\, \mu F$ across a $200\, V , 50\, Hz$ supply The power consumed by the lamp is $500\, W$ while the voltage drop across it is $100\, V$ Assume that there is no inductive load in the circuit Take $r m s$ values of the voltages The magnitude of the phase-angle (in degrees) between the current and supply voltage is $\phi $ Assume, $\pi \sqrt{3} \approx 5$ The value of $\phi$ is _____

A pendulum consists of a bob of mass $m =0.1\, kg$ and a massless inextensible string of length $L =1.0 \,m $. It is suspended from a fixed point at height $H =0.9 \,m$ above a frictionless horizontal floor Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension. A horizontal impulse $P =0.2\, kg - m / s$ is imparted to the bob at some instant. After the bob slides for some distance, the string becomes taut and the bob lifts off the floor. The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is $J \,kg - m ^{2} / s$. The kinetic energy of the pendulum just after the lift-off is $K$ Joules.

A Soft plastic bottle, filled with water of density $1\, gm / cc$, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure The test-tube has a mass of $5\, gm$, and it is made of a thick glass of density $25 \,gm / cc$ Initially the bottle is sealed at atmospheric pressure $p _{0}=10^{5} \,Pa$ so that the volume of the trapped air is $v _{0}=33\, cc$ When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces It is found that the test tube begins to sink at pressure $p _{0}+\Delta p$ without changing its orientation At this pressure, the volume of the trapped air is $v _{0}-\Delta v$ Let $\Delta v = X \,\,cc$ and $\Delta p = Y \times 10^{3} Pa$ The value of $X$ is _______

A pendulum consists of a bob of mass $m =01\, kg$ and a massless inextensible string of length $L =10 \,m $ It is suspended from a fixed point at height $H =09 \,m$ above a frictionless horizontal floor Initially, the bob of the pendulum is lying on the floor at rest vertically below the point of suspension A horizontal impulse $P =02\, kg - m / s$ is imparted to the bob at some instant After the bob slides for some distance, the string becomes taut and the bob lifts off the floor The magnitude of the angular momentum of the pendulum about the point of suspension just before the bob lifts off is $J \,kg - m ^{2} / s$ The kinetic energy of the pendulum just after the lift-off is $K$ Joules The value of $J$ is ______

A Soft plastic bottle, filled with water of density $1\, gm / cc$, carries an inverted glass test-tube with some air (ideal gas) trapped as shown in the figure. The test-tube has a mass of $5\, gm$, and it is made of a thick glass of density $25 \,gm / cc$. Initially the bottle is sealed at atmospheric pressure $p _{0}=10^{5} \,Pa$ so that the volume of the trapped air is $v _{0}=33\, cc$. When the bottle is squeezed from outside at constant temperature, the pressure inside rises and the volume of the trapped air reduces. It is found that the test tube begins to sink at pressure $p _{0}+\Delta p$ without changing its orientation. At this pressure, the volume of the trapped air is $v _{0}-\Delta v$.
Let $\Delta v = X \,\,cc$ and $\Delta p = Y \times 10^{3} Pa$

A cylindrical tube, with its base as shown in the figure, is filled with water It is moving down with a constant acceleration $a$ along a fixed inclined plane with angle $\theta=45^{\circ} P_{1}$ and $P_{2}$ are pressures at points $1$ and $2$, respectively located at the base of the tube. Let $\beta=\left(P_{1}-P_{2}\right) /(\rho g d)$, where $\rho$ is density of water, $d$ is the inner diameter of the tube and $g$ is the acceleration due to gravity. Which of the following statement(s) is(are) correct?

A long straight wire carries a current, $I =2$ ampere. A semi-circular conducting rod is placed beside it on two conducting parallel rails of negligible resistance. Both the rails are parallel to the wire. The wire, the rod and the rails lie in the same horizontal plane, as shown in the figure .Two ends of the semi-circular rod are at distances $1 \,cm$ and $4 \,cm$ from the wire. At time $t =0$, the rod starts moving on the rails with a speed $v =30\, m / s$ (see the figure)
A resistor $R =14 \,\Omega$ and a capacitor $C _{0}=50\, \mu F$ are connected in series between the rails At time $t =0, C _{0}$ is uncharged. Which of the following statement(s) is(are) correct? $[\mu_0 = 4 \pi \times 10^{-7}$ SI units. Take $ln_2=0.7]$

A long straight wire carries a current, 𝐼 = 2 ampere. A semi-circular conducting rod is placed beside

Which of the following statement(s) is(are) correct about the spectrum of hydrogen atom?

A particle of mass $M =02 \,kg$ is initially at rest in the $xy$-plane at a point $( x =-\ell, y =- h )$, where $\ell=10 \,m$ and $h =1\, m$. The particle is accelerated at time $t =0$ with a constant acceleration $a =10\, m / s ^{2}$ along the positive $x$-direction. Its angular momentum and torque with respect to the origin, in SI units, are represented by $\vec{ L }$ and $\vec{\tau}$ respectively. $\hat{ i }, \hat{ j }$ and $\hat{ k }$ are unit vectors along the positive $x , y$ and $z$-directions, respectively. If $\hat{k}=\hat{i} \times \hat{j}$ then which of the following statement(s) is(are) correct?

Two point charges $- Q$ and $\frac{+ Q }{ \sqrt{3}}$ are placed in the $xy$-plane at the origin $(0,0)$ and a point $(2,0)$, respectively, as shown in the figure. This results in an equipotential circle of radius $R$ and potential $V=0$ in the $x y$-plane with its center at $(b, 0)$. All lengths are measured in meters

Two point charges −𝑄 and +𝑄/√3 are placed in the xy-plane at the origin (0, 0) and a point (2, 0), respectively, as shown in the figure. This results in an equipotential circle of radius 𝑅 and potential 𝑉 = 0 in the xy-plane with its center at (b, 0). All lengths are measured in meters.

In the circuit shown below, the switch $S$ is connected to position $P$ for a long time so that the charge on the capacitor becomes $q _{1}\, \mu C$. Then $S$ is switched to position $Q$. After a long time, the charge on the capacitor is $q _{2}\, \mu C$

A projectile is thrown from a point $O$ on the ground at an angle $45^{\circ}$ from the vertical and with a speed $5 \sqrt{2} \,m / s$. The projectile at the highest point of its trajectory splits into two equal parts. One part falls vertically down to the ground, $05\, s$ after the splitting. The other part, $t$ seconds after the splitting, falls to the ground at a distance $x$ meters from the point $O$. The acceleration due to gravity $g =10 \,m / s ^{2}$.

Two concentric circular loops, one of radius $R$ and the other of radius $2 R$, lie in the $x y$-plane with the origin as their common centre, as shown in the figure . The smaller loop carries current $I_{1}$ in the anti-clockwise direction and the larger loop carries current $I_{2}$ in the clock wise direction, with $I_{2}>2 I_{1}, \vec{B}(x, y)$ denotes the magnetic field at a point $(x, y)$ in the $x y$-plane. Which of the following statement (s) is ( are ) correct?

A heavy nucleus $N$, at rest, undergoes fission $N \rightarrow P + Q$, where $P$ and $Q$ are two lighter nuclei Let $\delta= M _{ N }$ - $M_{P}-M_{Q}$, where $M_{P}, M_{Q}$ and $M_{N}$ are the masses of $P, Q$ and $N$, respectively $E _{P}$ and $E_{Q}$ are the kinetic energies of $P$ and $Q$, respectively. The speeds of $P$ and $Q$ are $v_{P}$ and $v_{Q}$, respectively If $c$ is the speed of light, which of the following statement(s) is(are) correct?

For a prism of prism angle 𝜃 = 60°, the refractive indices of the left half and the right half are, respectively, 𝑛₁ and 𝑛₂ (𝑛₂ ≥ 𝑛₁) as shown in the figure. The angle of incidence 𝑖 is chosen such that the incident light rays will have minimum deviation if 𝑛₁ = 𝑛₂ = 𝑛 = 1.5. For the case of unequal refractive indices, 𝑛₁ = 𝑛 and 𝑛₂ = 𝑛 +∆𝑛 (where∆𝑛≪𝑛), the angle of emergence 𝑒 =𝑖+∆𝑒. Which of the following statement(s) is (are) correct?