2024_1_Physics.pdf

JEE (Advanced) 2024 Paper 2 Physics SECTION 1  This section contains SIX (06) questions.  Each qu...

JEE (Advanced) 2024 Paper 2 Physics SECTION 1  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 If only (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 unanswered; Negative Marks : −2 In all other cases.  For example, in a question, if (A), (B) and (D) are the ONLY three options corresponding to correct answers, then choosing ONLY (A), (B) and (D) will get +4 marks; choosing ONLY (A) and (B) will get +2 marks; choosing ONLY (A) and (D) will get +2marks; choosing ONLY (B) and (D) will get +2 marks; choosing ONLY (A) will get +1 mark; choosing ONLY (B) will get +1 mark; choosing ONLY (D) will get +1 mark; choosing no option(s) (i.e. the question is unanswered) will get 0 marks and choosing any other option(s) will get −2 marks. FFFF Q.1 Consider a horizontal frictionless – plane shown in Figure. It is divided into two regions, and , by a line AB satisfying the equation =. The potential energy of a point particle of mass in region I is = 0 while it is in region II. The particle is sent from the origin O with speed along a line making an angle with the − axis. It reaches point P in region traveling with speed along a line that makes an angle with the −axis. Ignoring gravity and relativistic effects, which of the following statement(s) is/are TRUE ? (A) − (B) At the boundary there is an impulsive force in the – direction (C) At the boundary there is an impulsive force in the – direction (D) 1/10 JEE (Advanced) 2024 Paper 2 Q.2 Consider a system of units in which mass and torque are dimensionless. If length has a dimension of , which of the following statement(s) is/are TRUE ? (A) The dimension of linear momentum is (B) The dimension of angular momentum is (C) The dimension of surface tension is (D) The dimension of pressure is Q.3 A positive point charge is located inside a neutral hollow spherical conducting shell. The shell has inner radius and outer radius as shown in the figure; − is not negligible. The shell is centered on the origin. If the point charge is located at the origin in the center of the shell, then which of the following option(s) is/are correct ? (A) The electric potential at is (B) The magnitude of the electric field at is (C) The magnitude of the electric field from to is not equal (D) If the point charge were to be moved to the electric field for r > will be 2/10 JEE (Advanced) 2024 Paper 2 Q.4 Consider the experimental setup of a pair of long parallel metallic rails of negligible resistance placed horizontally apart with a distance. A horizontal metal rod of mass and resistance is placed perpendicularly on the rails at one of the ends. There is a uniform magnetic field directed perpendicular to the plane of the rod-rail arrangement. Let one end of the rail track is connected to a key and a capacitor of capacitance charged to voltage. At the key is closed. Neglect friction and self inductance of the loop. Then which of the following statement(s) is/are TRUE ? (A) where is charge on the capacitor at time (B) At = 0, where is the initial charge on the capacitor (C) The final velocity of the rod is (D) The final velocity of the rod is Q.5 A uniform solid sphere of mass m and radius r is placed at rest on a horizontal surface with coefficient of friction , as shown in the figure. The ball is given a horizontal impulse of fixed magnitude at a distance from its center, where , then which of the following statement(s) is/are TRUE ? (A) The final velocity of the sphere does not depend on (B) The final velocity of the sphere does not depend on (C) The sphere begins to roll without slipping for 2 (D) For = 0 and , the final velocity of the sphere is 3/10 JEE (Advanced) 2024 Paper 2 Q.6 One mole of an ideal gas undergoes a process as shown in the following − cycle where the cycle follows the path 2. The process 2 and are adiabatic and the whole cycle is carried out using air with adiabatic index.The compression factor is defined as the ratio of the largest and smallest volumes in the process and for this process Let denote the efficiency of the cycle and and denote the temperatures at points 2 and respectively, then the correct option(s) is/are ? (A) 2 (B) (C) (D) − 4/10 JEE (Advanced) 2024 Paper 2 SECTION 2 (Maximum Marks: 12)  This section contains TWO (02) question stems.  There are TWO (02) questions corresponding to each question stem.  The answer to each question is a NUMERICAL VALUE.  For each question, enter the correct numerical value corresponding to the answer in the designated place using the mouse and the on-screen virtual numeric keypad.  If the numerical value has more than two decimal places, truncate/round-off the value to TWO decimal places.  Answer to each question will be evaluated according to the following marking scheme: Full Marks : +3 If ONLY the correct numerical value is entered at the designated place; Zero Marks : 0 In all other cases. Question Stem for Question Nos. 7 and 8 Question Stem Consider an arrangement consisting of two uniform hemispheres with radius made of material of density 2. The top half is nailed to a support and the space between the two hemispheres is filled with water. The maximum distance between the two hemispheres so that the bottom half doesn’t fall is and the pressure difference between the top and bottom hemisphere is. Let mm and [Given: Surface tension of water is , acceleration due to gravity ( ) is and the contact angle between the material and water is respectively; Take ] Q.7 The value of is ________. Q.8 The value of is ________. 5/10 JEE (Advanced) 2024 Paper 2 Question Stem for Question Nos. 9 and 10 Question Stem A small box of mass is kept on a top of a frictionless ramp with a spring at height = from a horizontal table. The ramp is angled at to the horizontal on a table that is = 4 m above the floor. If the spring is pushed down by compared to its rest length, the box leaves the ramp at a speed m/s and lands at a distance meters away from the table. [Given: Spring constant acceleration due to gravity ; Assume friction is negligible] Q.9 The value of is ________. Q.10 The value of is ________. 6/10 JEE (Advanced) 2024 Paper 2 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 : − In all other cases. Q.11 A rod of uniform cross sectional area length and young’s modulus of elasticity is connected to a circuit as shown in the figure. It carries a constant current through with the voltage across the rod being measured by a voltmeter. The rod is stretched by application of a force at its ends. Neglecting any effects of Joule heating, which of the following graph represents the change in voltage across the rod as a function of stress , for small values of ? (A) (C) (D) 7/10 JEE (Advanced) 2024 Paper 2 Q.12 A ray of light enters an arrangement of prisms at grazing angle of incidence as shown in the figure. The arrangement contains five isosceles right angled prisms having refractive indices respectively. If the ray emerges out at a grazing angle then the refractive indices of the prism satisfy (A) (B) (C) 2 (D) − Q.13 Two masses separated by a distance are given initial velocities in opposite directions. Assume that the masses only interact through universal gravitation. If is the universal gravitational constant, then the condition at which the masses start following a closed orbit is (A) (B) (C) (D) 8/10 JEE (Advanced) 2024 Paper 2 Q.14 A beaker of radius is filled with mercury partly upto a height and is rotated about its axis with a constant angular velocity. The mercury surface attains a parabolic shape with radius of curvature. This mercury surface acts as a mirror for a point object kept at. Let origin be the pole of the mirror, then the − coordinate of the image is (A) (B) (C) (D) 9/11 Copyright © 2024 IIT Kanpur pur JEE (Advanced) 2024 Paper 2 SECTION 4 (Maximum Marks: 12)  This section contains FOUR (04) questions.  The answer to each question is a NUMERICAL VALUE.  For each question, enter the correct numerical value 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 value is entered; Zero Marks : 0 In all other cases. Q.15 A heater has a nickel heating filament with a temperature coefficient of resistance α = 0.0068 and with a resistance = 80 Ω at the room temperature = 293 K. After turning on the heater, the filament becomes red-hot at the temperature = 1000 K due to a current passing through it. Assuming that the filament transfers heat only by radiation (acts as a black body), the total surface area of the filament ( ) is _________. [Given: Stefan-Boltzmann constant = ] Q.16 A wedge of mass is kept at rest on a horizontal surface, and a block of mass is kept on the wedge at the height from the surface. The angle of the wedge is and there is no friction neither between the block and wedge nor between the surface and the wedge. The system is released into a free motion. If the time taken by the block to reach the horizontal surface is , then the value of is ________. [Given: 2 is the acceleration due to gravity] 10/11 Copyright © 2024 IIT Kanpur pur JEE (Advanced) 2024 Paper 2 Q.17 A source plays a tone with frequency = 400 Hz. A car is moving straight towards the source with a constant speed and the driver hears frequency = 420 Hz. Now if the source starts moving away from the car with a speed of 10 , the car starts moving with a constant speed towards it so that the driver hears the same frequency = 420 Hz, then the value of − is ________. [The speed of sound in air is ] END OF THE QUESTION PAPER 11/11 Copyright © 2024 IIT Kanpur pur