JEE Advanced Question Paper 2022 Physics Paper 2 solutions will be available on this page soon after the examination results are out. Students can access the JEE Advanced Question Paper 2022 Physics Paper 2 solved paper on this page. Each of these questions has been answered by the expert teachers at BYJU’S. All the questions are answered with in-depth explanations. Students can also download JEE Advanced Question Paper 2022 Physics Paper 2 with solutions in PDF form from this page.

## JEE Advanced 2022 Physics Question Paper 2 with Solutions

**SECTION – 1 (Maximum marks : 24)**

∙ This section contains **EIGHT (08) **questions.

∙ The answer to each question is a **SINGLE DIGIT INTEGER ranging from 0 TO 9, BOTH INCLUSIVE**.

∙ For each question, enter the correct integer corresponding to the answer using the mouse and the on-screen virtual numeric keypad in the place designated to enter the answer.

∙ Answer to each question will be evaluated according to the following marking scheme:

* Full Marks *: +3 If **ONLY **the correct integer is entered;

* Zero Marks *: 0 If the question is unanswered;

* Negative Marks *: −1 In all other cases.

**1. A particle of mass 1 kg is subjected to a force which depends on the position as **

**\(\begin{array}{l}\vec F = -k(x\hat i + y\hat j)\,\,{\rm{kg}}\,\,{\rm{m}}{{\rm{s}}^{{\rm{-2}}}}\end{array} \)**

**with\(\begin{array}{l}\vec r = \left( {\frac{1}{{\sqrt 2 }}\hat i + \sqrt 2 \hat j} \right)\,\,{\rm{m}}\ \text{and its velocity }\ \vec v = \left( {-\sqrt 2 \hat i + \sqrt 2 \hat j + \frac{2}{\pi }\hat k} \right)\,\,{\rm{m}}{{\rm{s}}^{-1}}.\end{array} \) Let **

*k*= 1 kg s^{–2}. At time*t*= 0, the particle’s position*v*and_{x}*v*denote the_{y}*x*and the*y*components of the particle’s velocity, respectively. Ignore gravity. When*z*= 0.5 m, the value of (*xv*–_{y}*yv*) is _______ m_{x}^{2}s^{–1}.**Answer (3)**

**Sol. ***F _{x}* = –

*x*=

*ma*.

_{x}So

and

at *t* = 0,

So

and

and

Similarly

*F _{y}* = –

*y*=

*ma*.

_{y}So, *y* = *A _{y}* sin(ωt + φ

_{y}) (ω = 1 rad/s)

and

at *t* = 0, y = √2 m and v_{y} = √2 m/s

So

and

_{y}= 2 (3 and 4).

So, (*xv _{y}* –

*yv*)

_{x}= 3

**2. In a radioactive decay chain reaction, **

**\(\begin{array}{l}_{90}^{230}{\rm{Th}}\ \text{nucleus decays into}\ _{84}^{214}{\rm{Po}}\ \text{nucleus}.\end{array} \)**

**The ratio of the number of α to number of β**

^{–}particles emitted in this process is _______.**Answer (2)**

**Sol.** Let number of α particles are *n*_{α} and β particles are *n*_{β} so

4*n*_{α} = 230 – 214

⇒ *n*_{α} = 4

*n*_{β} = 84 – (90 – 2*n*_{α})

*n*_{β} = 2

So

**3. Two resistances R_{1} = X Ω and R_{2} = 1 Ω are connected to a wire AB of uniform resistivity, as shown in the figure. The radius of the wire varies linearly along its axis from 0.2 mm at A to 1 mm at B. A galvanometer (G) connected to the center of the wire, 50 cm from each end along its axis, shows zero deflection when A and B are connected to a battery. The value of X is _______.**

**Answer (5)**

**Sol. **Resistance of frustum shaped conductor shown is

For the shown conductor in the diagram.

thus, the resistance of left half is

and the resistance of right half is

for Wheatstone to be balanced

⇒ *X* = 5

**4. In a particular system of units, a physical quantity can be expressed in terms of the electric charge e, electron mass m_{e}, Planck’s constant h, and Coulomb’s constant **

**\(\begin{array}{l}k = \frac{1}{{4\pi {\varepsilon _0}}},\end{array} \)**

**where ε**

_{0}is the permittivity of vacuum. In terms of these physical constants, the dimension of the magnetic field is [*B*] = [*e*]^{α}[*m*]_{e}^{β }[*h*]^{γ }[*k*]^{δ}. The value of α + β + γ + δ is ______.**Answer (4)**

**Sol.** [*B*] = [*e*]^{α} [*m _{e}*]

^{β}[

*h*

^{γ}] [

*k*]

^{δ}

*M*

^{1}

*T*

^{–2}

*I*

^{–1}] = [

*IT*]

^{α}[

*M*]

^{β}[

*ML*

^{2}T^{–1}]

^{γ}[

*ML*

^{3}

*T*]

^{–4}^{δ}

So, β + γ + δ = 1 …(i)

2γ + 3δ = 0 …(ii)

α – γ – 4δ = –2 …(iii)

α – 2δ = –1 …(iv)

On solving

so, α + β + γ + δ = 4

**5. Consider a configuration of n identical units, each consisting of three layers. The first layer is a column of air of height h = ⅓ cm, and the second and third layers are of equal thickness **

**\(\begin{array}{l}d = \frac{\sqrt3- 1}{2}{\rm{ cm,}}\ \text{and refractive indices}\ {\mu _1} = \sqrt {\frac{3}{2}}\ {\rm{ and }}\ {\mu _2} = \sqrt 3 ,\end{array} \)**

**respectively. A light source\(\begin{array}{l}l = \frac{8}{{\sqrt 3 }}{\rm{ cm,}}\end{array} \) as shown in the figure. The value of **

*O*is placed on the top of the first unit, as shown in the figure. A ray of light from*O*is incident on the second layer of the first unit at an angle of θ = 60° to the normal. For a specific value of*n*, the ray of light emerges from the bottom of the configuration at a distance*n*is _______.**Answer (4)**

**Sol.**

and,

⇒ θ_{2} = 45°

⇒ *x*_{2} = *d*

and,

⇒ θ_{3} = 30°

**6. A charge q is surrounded by a closed surface consisting of an inverted cone of height h and base radius R, and a hemisphere of radius R as shown in the figure. The electric flux through the conical surface is **

**\(\begin{array}{l}\frac{{nq}}{{6{\varepsilon _0}}}\ \text{(in SI units)}.\end{array} \)**

**The value of**

*n*is _________.**Answer (3)**

**Sol.**

** φ **through cone

** ∴ ***n* = 3

**7. On a frictionless horizontal plane, a bob of mass m = 0.1 kg is attached to a spring with natural length l_{0} = 0.1 m. The spring constant is k_{1} = 0.009 Nm^{–1} when the length of the spring l > l_{0} and is k_{2} = 0.016 Nm^{–1} when l < l_{0}. Initially the bob is released from l = 0.15 m. Assume that Hooke’s law remains valid throughout the motion. If the time period of the full oscillation is T = (n π) s, then the integer closest to n is _______.**

**Answer (6)**

**Sol. **

= 5.83π

**8. An object and a concave mirror of focal length f = 10 cm both move along the principal axis of the mirror with constant speeds. The object moves with speed V_{0} = 15 cm s^{–1} towards the mirror with respect to a laboratory frame. The distance between the object and the mirror at a given moment is denoted by u. When u = 30 cm, the speed of the mirror V_{m} is such that the image is instantaneously at rest with respect to the laboratory frame, and the object forms a real image. The magnitude of V_{m} is _____ cm s^{–1}.**

**Answer (3)**

**Sol. **

= 3 cm/s

**SECTION – 2 (Maximum marks : 24)**

∙ This section contains **SIX (06) **questions.

∙ Each question has **FOUR **options (A), (B), (C) and (D). **ONE OR MORE THAN ONE **of these four option(s) is (are) correct answer(s).

∙ For each question, choose the option(s) corresponding to (all) the correct answer(s).

∙ Answer to each question will be evaluated according to the following marking scheme:

* Full Marks : *+4 **ONLY **if (all) the correct option(s) is(are) chosen;

* Partial Marks : *+3 If all the four options are correct but **ONLY **three options are chosen;

* Partial Marks : *+ 2 If three or more options are correct but **ONLY **two options are chosen, both of which are correct;

* Partial Marks : *+1 If two or more options are correct but **ONLY **one option is chosen and it is a correct option;

* Zero Marks : *0 If none of the options is chosen (i.e. the question is unanswered);

* Negative Marks : *–2 In all other cases.

**9. In the figure, the inner (shaded) region A represents a sphere of radius r_{A} = 1, within which the electrostatic charge density varies with the radial distance r from the center as ρ_{A} = kr, where k is positive. In the spherical shell B of outer radius r_{B}, the electrostatic charge density varies as ρ_{B} =2k/r. Assume that dimensions are taken care of. All physical quantities are in their SI units. **

** Which of the following statement(s) is/(are) correct?**

(A) If

*B*.

(B) If

*B*is

(C) If *r _{B}* = 2, then the total charge of the configuration is 15π

*k*.

(D) lf

*B*is

**Answer (B)**

**Sol. **

If

If

(B) is correct

If *r _{B}* = 2

= 13π*k*

Option (C) is incorrect

If

**10. In Circuit-1 and Circuit-2 shown in the figures, R_{1} = 1 Ω, R_{2} = 2 Ω and R_{3} = 3 Ω. **

*P*_{1} and *P*_{2} are the power dissipations in Circuit-1 and Circuit-2 when the switches S_{1} and S_{2} are in open conditions, respectively.

*Q*_{1} and *Q*_{2} are the power dissipations in Circuit-1 and Circuit-2 when the switches S_{1} and S_{2} are in closed conditions, respectively.

** Which of the following statement(s) is(are) correct?**

(A) When a voltage source of 6 V is connected across A and B in both circuits, *P*_{1} < *P*_{2}

(B) When a constant current source of 2 Amp is connected across A and B in both circuits, *P*_{1} > *P*_{2}

(C) When a voltage source 6 V is connected across A and B in Circuit-1, *Q*_{1} > *P*_{1}

(D) When a constant current source of 2 Amp is connected across A and B in both circuits, *Q*_{2} < *Q*_{1}

**Answer (A, B, C)**

**Sol. **

When S_{1} and S_{2} are open

Option (A) is correct.

⇒ If 2 A source is used in both the cases.

*P*_{1} > *P*_{2}

Option (B) is correct

For *Q*_{1}

*P*_{1} = 24.75 W

*Q*_{1} > *P*_{1}

Option (C) is correct.

For option (D)

*Q*_{2} > *Q*_{1}

Option (D) is incorrect.

**11. A bubble has surface tension S. The ideal gas inside the bubble has ratio of specific heats γ = 5/3. The bubble is exposed to the atmosphere and it always retains its spherical shape. When the atmospheric pressure is P_{a}_{1}, the radius of the bubble is found to be r_{1} and the temperature of the enclosed gas is T_{1}. When the atmospheric pressure is P_{a}_{2}, the radius of the bubble and the temperature of the enclosed gas are r_{2} and T_{2}, respectively.**

** Which of the following statement(s) is(are) correct?**

(A) If the surface of the bubble is a perfect heat insulator, then

(B) If the surface of the bubble is a perfect heat insulator, then the total internal energy of the bubble including its surface energy does not change with the external atmospheric pressure.

(C) If the surface of the bubble is a perfect heat conductor and the change in atmospheric temperature is negligible, then

(D) If the surface of the bubble is a perfect heat insulator, then

**Answer (C, D)**

**Sol. ***S* : Surface tension

When,

For adiabatic process

___________________

For option (B) Total internal energy + surface energy will not be same as word done by gas will be there.

Option (B) is incorrect.

For option (C)

Option (C) is correct

**12. A disk of radius R with uniform positive charge density σ is placed on the xy plane with its center at the origin. The Coulomb potential along the z-axis is**

** **

**\(\begin{array}{l}V(z) = \frac{\sigma }{{2{ \in _0}}}\left( {\sqrt {{R^2} + {z^2}} -z} \right)\end{array} \)**

** A particle of positive charge q is placed initially at rest at a point on the z-axis with z = z_{0} and z_{0} > 0. In addition to the Coulomb force, the particle experiences a vertical force **

**\(\begin{array}{l}\overrightarrow F=-c\ \hat k\ \text{with}\ c > 0.\ \text{Let}\ \beta=\frac{{2c{\in _0}}}{{q\sigma }}.\end{array} \)**

**Which of the following statement(s) is(are) correct?**

(A) For

(B) For

(C) For

*z*=

*z*

_{0}

(D) For β > 1 and z_{0} > 0, the particle always reaches the origin.

**Answer (A, C, D)**

**Sol. **

U_{z} = cz

At *z* = 0,

At z = z_{0} = 25/7 R, β = ¼

At z = z_{0} = 3/7 R, β = ¼

⇒ In option (A) particle reaches at origin with positive kinetic energy

⇒ In option B at *U*(*z*)_{net}

⇒ The kinetic energy at origin will become negative

⇒ In option (C),

*z*= 0,

And

⇒ Particle will return back to *z*_{0}.

In option (D) (β > 1 and z_{0} > 0)

U(z)_{net }will keep on increasing with *z*

⇒ Particle always reaches the origin.

⇒ Answer (A, C, D)

**13. A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index n_{2}. The other slit is at the interface of this medium with another medium 1 of refractive index n_{1} (≠ n_{2}). The line joining the slits is perpendicular to the interface and the distance between the slits is d. The slit widths are much smaller than d. A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle θ from the line joining them, so that θ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.**

** Which of the following statement(s) is(are) correct?**

(A) The phase difference between the two rays is independent of d.

(B) The two rays interfere constructively at the detector.

(C) The phase difference between the two rays depends on n_{1} but is independent of n_{2}.

(D) The phase difference between the two rays vanishes only for certain values of d and the angle of incidence of the beam, with q being the corresponding angle of refraction.

**Answer (A, B)**

**Sol. **

*AB* = (*d*)(tanθ)

and *BC* = *AB* sinα = (*d*) (tanθ)(sinα)

Also, *AD* = *AB* sinθ

⇒ Path difference (in vaccum)

= *n*_{1}*BC* – *n*_{2}*AD*

= *n*_{1}(*AB*) sinα – *n*_{2}(*AB* sinθ)

= *AB* (*n*_{1 }sinα – *n*_{2 }sinθ) = 0

⇒ (A), (B) are correct

(C), (D) are incorrect.

**14. In the given P–V diagram, a monoatomic gas (γ = 5/3) is first compressed adiabatically from state A state B. Then it expands isothermally from state B to state C. [Given : **

**\(\begin{array}{l}{\left( {\frac{1}{3}} \right)^{0.6}}\; \simeq \;0.5,\;{\rm{In}}\;2\; \simeq \;0.7\end{array} \)**

**].**

** Which of the following statement(s) is(are) correct?**

(A) The magnitude of the total work done in the process *A* → *B* → *C* is 144 kJ.

(B) The magnitude of the work done in the process *B* → *C* is 84 kJ.

(C) The magnitude of the work done in the process *A* → *B* is 60 kJ.

(D) The magnitude of the work done in the process *C* → *A* is zero.

**Answer (B, C, D)**

**Sol.***Pv*^{γ} = *c*

= – 60 kJ

⇒ (C) is correct

*C* → *A* is isochoric ⇒ (D) is correct

*BC* : *W _{BC}*

= 79 kJ

⇒ (A) & (B) are not correct.

**SECTION – 3 (Maximum marks : 12)**

∙ This section contains **FOUR (04) **questions.

∙ Each question has **FOUR **options (A), (B), (C) and (D). **ONLY ONE **of these four options is the correct answer.

∙ For each question, choose the option corresponding to the correct answer.

∙ Answer to each question will be evaluated according to the following marking scheme:

Full Marks : +3 If **ONLY** the correct option is chosen;

Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered);

Negative Marks : −1 In all other cases.

**15. A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the circumference of A, as shown in the figure. A flat surface of B also lies on the plane of the table. The center of mass of B has fixed angular speed ω about the vertical axis passing through the center of A. The angular momentum of B is nMωR^{2} with respect to the center of A. Which of the following is the value of n?**

(A) 2

(B) 5

(C) 7/2

(D) 9/2

**Answer (B)**

**Sol.** Angular momentum of *B* with respect to center of *A*

Comparing the magnitude with *nM*ω*R*^{2}

*n* = 5

**16. When light of a given wavelength is incident on a metallic surface, the minimum potential needed to stop the emitted photoelectrons is 6.0 V. This potential drops to 0.6 V if another source with wavelength four times that of the first one and intensity half of the first one is used. What are the wavelength of the first source and the work function of the metal, respectively? [Take hc/e = 1.24 × 10 ^{–6} J m C^{–1}.]**

(A) 1.72 x 10^{–7} m, 1.20 eV

(B) 1.72 x 10^{–7} m, 5.60 eV

(C) 3.78 x 10^{–7} m, 5.60 eV

(D) 3.78 x 10^{–7} m, 1.20 eV

**Answer (A)**

**Sol. **

= 1.72 × 10^{–7} m

⇒ from equation (i)

**17. Area of the cross-section of a wire is measured using a screw gauge. The pitch of the main scale is 0.5 mm. The circular scale has 100 divisions and for one full rotation of the circular scale, the main scale shifts by two divisions. The measured readings are listed below.**

Measurement condition |
Main scale reading |
Circular scale reading |
---|---|---|

Two arms of gauge touching each other without wire | 0 division | 4 divisions |

Attempt-1: With wire | 4 divisions | 20 divisions |

Attempt-2: With wire | 4 divisions | 16 divisions |

** What are the diameter and cross-sectional area of the wire measured using the screw gauge?**

(A) 2.22 ± 0.02 mm, π (1.23 ± 0.02) mm^{2}

(B) 2.22 ± 0.01 mm, π (1.23 ± 0.01) mm^{2}

(C) 2.14 ± 0.02 mm, π (1.14 ± 0.02) mm^{2}

(D) 2.14 ± 0.01 mm, π (1.14 ± 0.01) mm^{2}

**Answer (C*) (Bonus declared by JEE) **

**Sol.****Reading-1**

MSR = 4 × 0.5 = 2 mm

Zero error

R_{1} = MSR + CSR – (Zero error)

= (2 + 0.20 – 0.04) mm

= 2.16 mm

** Reading-2**

MSR = 2 mm

CSR = 0.16 mm

Zero error = 0.04 mm

R_{2} = (2 + 0.16 – 0.04) mm = 2.12 mm

Reading/average

_{m}(say)

Average mean error

⇒ Diameter = (2.14 ± 0.02) mm = d (say)

Area

**18. Which one of the following op****tions represents the magnetic field **

**\(\begin{array}{l}\vec B \end{array} \)**

**at**

*O*due to the current flowing in the given wire segments lying on the*xy*plane?(A)

(B)

(C)

**Answer (C)**

**Sol.***B*_{net}* = B*_{semicircle}* + B*_{quarter}* + B*_{straight}

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