JEE Advanced Previous Year Questions (2018 - 2023): Properties of Matter | Physics for JEE Main & Advanced PDF Download

2023

Ans: 25

=

= 25 cm

2022

Q1: 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_a1, the radius of the bubble is found to be r₁ and the temperature of the enclosed gas is T₁. When the atmospheric pressure is P_a2, the radius of the bubble and the temperature of the enclosed gas are r₂ and T_2, respectively.      [JEE Advanced 2022 Paper 2]
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 .
Ans: (c) & (d)
For adiabatic process:

Also,

At same temperature,

Q2: An ideal gas of density   ρ = 0.2 kg m−3 enters a chimney of height ℎ at the rate of α =   0.8 kg s⁻¹ from its lower end, and escapes through the upper end as shown in the figure. The cross-sectional area of the lower end is  A₁=0.1 m² and the upper end is  A₂ = 0.4 m². The pressure and the temperature of the gas at the lower end are  600 Pa and  300 K, respectively, while its temperature at the upper end is  150 K. The chimney is heat insulated so that the gas undergoes adiabatic expansion. Take g = 10 m s⁻² and the ratio of specific heats of the gas γ = 2. Ignore atmospheric pressure. 

Which of the following statement(s) is(are) correct?
(a) The pressure of the gas at the upper end of the chimney is  300 Pa.
(b) The velocity of the gas at the lower end of the chimney is   40 m s⁻¹ and at the upper end is  20 ms⁻¹.
(c) The height of the chimney is  590 m.
(d) The density of the gas at the upper end is   0.05 kg m⁻³.     [JEE Advanced 2022 Paper 1]
Ans: (b)
Given g = 10 m s⁻² and the ratio of specific heats of the gas γ = 2
The process described is adiabatic. In an adiabatic process (a process during which no heat is gained or lost), the following relationship holds:

Where :
- P₁ and P₂ are the initial and final pressures,
- T₁ and T₂ are the initial and final temperatures,
- γ is the ratio of specific heats (given as 2). 
Given that,

Using the ideal gas law in the form ρ = PM/RT (where R is the specific gas constant), and rearranging to find the relationship between ρ₁ and ρ₂ :

Next, use the principle of conservation of mass flow rate to determine the velocity of the gas at the lower and upper ends. 

Similarly, for the upper end :

Work done on the gas = total energy = ΔK + ΔU +  internal energy 

3000 = -600 + 10 h
10h = 3000 + 600
h = 360 m

2021

(a)
(b)
(c)
(d)         [JEE Advanced 2021 Paper 1]
Ans: (a) & (c)

2020

Q1: A train with cross-sectional area S_t is moving with speed vt inside a long tunnel of cross-sectional area S₀ (S₀ = 4S_t). Assume that almost all the air (density ρ) in front of the train flows back between its sides and the walls of the tunnel. Also, the air flow with respect to the train is steady and laminar. Take the ambient pressure and that inside the train to be p₀. If the pressure in the region between the sides of the train and the tunnel walls is p, then
p₀ - p = . The value of 𝑁 is ________.               [JEE Advanced 2020 Paper 2]
Ans:

Applying Bernoulli's equation,

From equation of continuity,

From Eqs. (i) and (ii), we get

∴ N = 9

Q2: A hot air balloon is carrying some passengers, and a few sandbags of mass 1 kg each so that its total mass is 480 kg. Its effective volume giving the balloon its buoyancy is V. The balloon is floating at an equilibrium height of 100 m. When N number of sandbags are thrown out, the balloon rises to a new equilibrium height close to 150 m with its volume V remaining unchanged. If the variation of the density of air with height h from the ground is  , where ρ₀ = 1.25 kg m⁻³ and h₀ = 6000 m, the value of N is _________.              [JEE Advanced 2020 Paper 2]
Ans: 4
Weight = Upthrust

Dividing Eq. (i) by Eq. (ii), we get

N = 4

Q3: A cubical solid aluminium (bulk modulus = ) block has an edge length of 1 m on the surface of the earth. It is kept on the floor of a 5 km deep ocean. Taking the average density of water and the acceleration due to gravity to be 10³ kg m^-3 and 10 ms^-2, respectively, the change in the edge length of the block in mm is _______.             [JEE Advanced 2020 Paper 2]
Ans: 0.24
 (where, B = bulk modulus)

Substituting the given values, we get Δl = 0.24 mm 

Q4: When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are 10³ kg m⁻³ , 0.07 Nm⁻¹ and 10 ms⁻² , respectively, the value of h (in mm) is _________.     
[JEE Advanced 2020 Paper 1]

Ans: 3.74

Pressure at the bottom of disc = Pressure due to surface tension

h = √14 mm = 3.741

Q4: An open-ended U-tube of uniform cross-sectional area contains water (density 10³ kg m⁻³ ). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg m⁻³ is added to the left arm until its length is 0.1 m, as shown in the schematic figure below. The ratio (ℎ1/ℎ2) of the heights of the liquid in the two arms is : 

(a) 15/14
(b) 35/33
(c) 7/6
(d) 5/4              [JEE Advanced 2020 Paper 1]
Ans: (b)
We have, h₁ + h₂ = 0.29 × 2 + 0.1
h₁ + h₂ = 0.68 .......(i)
⇒ p₀ + ρ_kg(0.1) +ρ_wg(h₁ − 0.1) − ρ_wgh₂ = p₀
where, ρ_k = density of kerosene and ρ_w = density of water.
⇒ ρ_kg(0.1) + ρ_wgh₁ − ρ_wg × (0.1) = ρ_wgh₂
⇒ 800 × 10 × 0.1 + 1000 × 10 × h₁ − 1000 × 10 × 0.1 = 1000 × 10 × h₂
⇒ 10000(h₁ − h₂) = 200
⇒ h₁ − h₂ = 0.01 .......(ii)
Solving Eqs. (i) and (ii), we get
h₁ = 0.35
and h₂ = 0.33
So, h₁ / h₂ = 35/33

2019

Ans: 2

= 2.00

Q2: A liquid at 30∘C is poured very slowly into a Calorimeter that is at temperature of 110^∘C. The boiling temperature of the liquid is 80^∘C. It is found that the first 5 gm of the liquid completely evaporates. After pouring another 80 gm of the liquid the equilibrium temperature is found to be 50^∘C. The ratio of the latent heat of the liquid to its specific heat will be ...........^∘C.
[Neglect the heat exchange with surrounding]        [JEE Advanced 2019 Paper 1]
Ans: 270
Case - I 5C × 50 + 5L = C₂ × 30 ....(i)
Case - II 80C[50 − 30] = C₂ [80 − 50] ....(ii)
By Eq. (i) and (ii)
1600C = 250 + 5L 

Q3: A current carrying wire heats a metal rod. The wire provides a constant power (P) to the rod. The metal rod is enclosed in an insulated container. It is observed that the temperature (T) in the metal rod changes with time (t) as  where β is a constant with appropriate dimension while T₀ is a constant with dimension of temperature. The heat capacity of the metal is
(a)
(b)
(c)
(d)        [JEE Advanced 2019 Paper 1 ]
Ans: (b)
Heat Capacity,

Power of the rod,

Substituting this value of t^3/4 in equation (i) we get, 

2018

Q1: Two conducting cylinders of equal length but different radii are connected in series between two heat baths kept at temperatures T₁ = 300K and T₂ = 100K, as shown in the figure. The radius of the bigger cylinder is twice that of the smaller once and the thermal conductivities of the materials of the smaller and the larger cylinders are K₁ and K₂ respectively. If the temperature at the junction of the two cylinders in the steady state is 200 K, then K₁/K₂= ______________.      [JEE Advanced 2018 Paper 1]

Ans: 4
The intermediate temperature is given by the formula

Here, T = 200 k, T₁ = 300 k, T₂ = 100 k, l₁ = l₂ and A₁ = πr², A₂ = 4πr² 

∴ 200 k₁ + 800 k₂ = 300 k₁ + 400 k
⇒ 400 k₂ = 100 k₁
∴ k₁ / k₂ = 4.0
Q2: Consider a thin square plate floating on a viscous liquid in a large tank. The height ℎ of the liquid in the tank is much less than the width of the tank. The floating place is pulled horizontally with a constant velocity μ₀. Which of the following statements is (are) true?   [JEE Advanced 2018 Paper 2]
(a) The resistive force of liquid on the plate is inversely proportional to ℎ
(b) The resistive force of liquid on the plate is independent of the area of the plate
(c) The tangential (shear) stress on the floor of the tank increases with μ₀
(d) The tangential (shear) stress on the plate varies linearly with the viscosity η of the liquid
Ans: (c) & (d)

Force of viscosity can be written as follows:

Here η is coefficient of viscosity, A is face area of plate and dv / dy is velocity gradient. We can assume that velocity of fluid at the bottom (h depth below) is zero; hence ; hence force of viscocity can be written as follows:

We can see that force of viscosity is inversely proportional to h; hence option (a) is correct.
We can see that force of viscosity is proportional to area of plate; hence option (b) is wrong.
Tangential stress can be written as
We can see that options (c) and (d) are also correct.

Q3: A uniform capillary tube of inner radius r is dipped vertically into a beaker filled with water. The water rises to a height ℎ in the capillary tube above the water surface in the beaker. The surface tension of water is σ. The angle of contact between water and the wall of the capillary tube is θ. Ignore the mass of water in the meniscus. Which of the following statements is (are) true?
(a) For a given material of the capillary tube, ℎ decreases with increase in r
(b) For a given material of the capillary tube, ℎ is independent of σ
(c) If this experiment is performed in a lift going up with a constant acceleration, then ℎ decreases
(d) ℎ is proportional to contact angle θ            [JEE Advanced 2018 Paper 1]
Ans: (a) & (c)
We know that, 

where r is inner radius of capillary tube; σ is surface tension; θ is angle between water and wall of capillary tube; h is height of water in capillary tube and g is acceleration due to gravity. From Eq. (1), 

Therefore, for a given material of the capillary tube, h decreases with increase in r.
Hence, option (A) is correct.
h depends on σ, therefore option (B) is incorrect.
In a lift going up with a constant acceleration a, the force due to surface tension remains same but weight of the water increases i.e., W_lift = πr²hρ(g + a). Thus, the height of the water rise in a capillary becomes

where g_eff is the effective g in the lift. Hence, h decrease if the experiment is performed in a lift going up with a constant acceleration.
From (1), h ∝ cosθ and not θ, therefore, option (D) is incorrect.