Practice Questions

Q10.An aluminium rod with Young’s modulus Y = 7. 0 × 1010 N m−2 undergoes elastic strain of 0. 04%. The energy per unit volume stored in the rod in SI unit JEE Main 2023 (08 Apr Shift 1) JEE Main Previous Year Paper (1) 2800 (2) 11200 (3) 5600 (4) 8400

Q10.The surface tension of soap solution is 3. 5 × 10−2 N m−1 . The amount of work done required to increase the radius of soap bubble from 10 cm to 20 cm is _____ ×10−4 J . (take π = 227 )

Q10.A steel rod of length 1 m and cross-sectional area 10−4 m2 is heated from 0°C to 200°C without being allowed to extend or bend. The compressive tension produced in the rod is _____ ×104 N . (Given Young's modulus of steel = 2 × 1011 N m−2 , coefficient of linear expansion = 10−5 K−1 )

Q11.A spherical ball of radius 1 mm and density 10. 5 g cc−1 is dropped in glycerine of coefficient of viscosity 9. 8 poise and density 1. 5 g cc−1 . Viscous force on the ball when it attains constant velocity is 3696 × 10−x N . The value of x is (Given, g = 9. 8 m s−2 and π = 227 )

Q11.A parallel plate capacitor of capacitance 2 F is charged to a potential 𝑉. The energy stored in the capacitor is 𝐸1. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The 𝐸2 energy stored in the combination is 𝐸2. The ratio is 𝐸1 (1) 2: 1 (2) 2: 3 (3) 1: 2 (4) 1: 4

Q11.Let 𝜎 be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region 𝐸𝐼 , 𝐸𝐼𝐼 and 𝐸𝐼𝐼𝐼 (1) → 𝐸𝐼= 2𝜎 ^𝑛, →𝐸𝐼𝐼= 0, →𝐸𝐼𝐼𝐼= 2𝜎 ^𝑛 (2) →𝐸𝐼= 0, →𝐸𝐼𝐼= 𝜎 ^𝑛, →𝐸𝐼𝐼𝐼= 0 ∈0 ∈0 ∈0 → 𝜎 → → 𝜎 → -𝜎 → → 𝜎 (3) ^𝑛 𝐸𝐼= ^𝑛, 𝐸𝐼𝐼= 0, 𝐸𝐼𝐼𝐼= 𝐸𝐼= 2 ∈0 ^𝑛, 𝐸𝐼𝐼= 0, 𝐸𝐼𝐼𝐼= 2 ∈0 ^𝑛 (4) ∈0 ∈0

Q11.As shown in the figure, a network of resistors is connected to a battery of 24 V with an internal resistance of 3 𝛺. The currents through the resistors 𝑅4 and 𝑅5 are 𝐼4 and 𝐼5 respectively. The values of 𝐼4 and 𝐼5 are: 8 2 24 6 (1) 𝐼4 = 5 A and I5 = 5 A (2) 𝐼4 = 5 A and 𝐼5 = 5 A (3) 𝐼4 = 6 A and 𝐼5 = 24 A (4) 𝐼4 = 2 A and 𝐼5 = 8 A 5 5 5 5

Q11. A bowl filled with very hot soup cools from 98°C to 86∘C in 2 minutes when the room temperature is 22∘C . How long it will take to cool from 75∘C to 69∘C ? (1) 2 minute (2) 1. 4 minute (3) 0. 5 minute (4) 1 minute

Q11.An air bubble of volume 1 cm3 rises from the bottom of a lake 40 m deep to the surface at a temperature of 12°C. The atmospheric pressure is 1 × 105 Pa, the density of water is 1000 kg m−3 and g = 10 m s−2. There is no difference of the temperature of water at the depth of 40 m and on the surface. The volume of air bubble when it reaches the surface will be (1) 2 cm3 (2) 3 cm3 (3) 4 cm3 (4) 5 cm3

Q11.Two isolated metallic solid spheres of radii 𝑅 and 2𝑅 are charged such that both have same charge density 𝜎 . The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is 𝜎'. 𝜎' The ratio is : 𝜎 9 4 (1) (2) 4 3 5 5 (3) (4) 3 6

Q11.A metal block of base area 0. 20 m2 is placed on a table, as shown in figure. A liquid film of thickness 0. 25 mm is inserted between the block and the table. The block is pushed by a horizontal force of 0. 1 N and moves with a constant speed. If the viscosity of the liquid is 5. 0 × 10–3 Pl, the speed of block is ______ ×10−3 m s−1 .

Q11. The figure shows a liquid of given density flowing steadily in horizontal tube of varying cross-section. Cross- sectional areas at A is 1. 5 cm2, and B is 25 mm2, if the speed of liquid at B is 60 cm s−1 then (PA–PB) is (Given PA and PB are liquid pressures at A and B points. Density ρ = 1000 kg m−3 A and B are on the axis of tube) (1) 135 Pa (2) 27 Pa (3) 175 Pa (4) 36 Pa 5 ) 2 v, when v is the average

Q11.Work done by a Carnot engine operating between temperatures 127°C and 27°C is 2 kJ . The amount of heat transferred to the engine by the reservoir is: (1) 8 kJ (2) 2. 67 kJ (3) 2 kJ (4) 4 kJ

Q11.The surface of water in a water tank of cross section area 750 cm2 on the top of a house is h m. above the tap level. The speed of water coming out through the tap of cross section area 500 mm2 is 30 cm s−1 . At that instant, dh is x × 10−3 m s−1 . The value of x will be ______. dt

Q11.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Efficiency of a reversible heat engine will be highest at –273 °C temperature of cold reservoir. Reason R : The efficiency of Carnot’s engine depends not only on temperature of cold reservoir but it depends on the temperature of hot reservoir too and is given as η = (1 −T2T1 ) In the light of the above statements, choose the correct answer from the options given below : (1) A is true but R is false (2) Both A and R are true but R is NOT the correct explanation of A (3) A is false but R is true (4) Both A and R are true and R is the correct explanation of A

Q11.A body cools in 7 minutes from 60oC to 40oC. The temperature of the surrounding is 10oC. The temperature of the body after the next 7 minutes will be (1) 30oC (2) 32oC (3) 34oC (4) 28oC

Q11.Which of the following correctly represents the variation of electric potential ( 𝑉) of a charged spherical conductor of radius ( 𝑅) with radial distance ( 𝑟) from the centre? (1) (2) (3) (4)

Q11. A 10 𝜇C charge is divided into two parts and placed at 1 cm distance so that the repulsive force between them is maximum. The charges of the two parts are: (1) 7𝜇C, 3𝜇C (2) 8𝜇C, 2𝜇C (3) 5𝜇C, 5𝜇C (4) 9𝜇C, 1𝜇C

Q11.Heat energy of 735 J is given to a diatomic gas allowing the gas to expand at constant pressure. Each gas molecule rotates around an internal axis but do not oscillate. The increase in the internal energy of the gas will be: (1) 525 J (2) 441 J (3) 572 J (4) 735 J

Q11.According to law of equipartition of energy the molar specific heat of a diatomic gas at constant volume where the molecule has one additional vibrational mode is :- (1) 9 R (2) 5 R 2 2 (3) 3 R (4) 7 R 2 2

Q12.An air bubble of diameter 6 mm rises steadily through a solution of density 1750 kg m−3 at the rate of 0. 35 cm s−1 . The co-efficient of viscosity of the solution (neglect density of air) is ________ Pas (given, g = 10 m s−2 ).

Q12.The graph between two temperature scales P and Q is shown in the figure. Between upper fixed point and lower fixed point there are 150 equal divisions of scale P and 100 divisions on scale Q. The relationship for conversion between the two scales is given by : . JEE Main 2023 (25 Jan Shift 2) JEE Main Previous Year Paper tQ (1) 150 = tP−180100 (2) 100tQ = tP−30150 (3) 180 tP = tQ−40100 (4) 100tQ = tP−180150

Q12.The equivalent resistance between 𝐴 𝑎𝑛𝑑 𝐵 of the network shown in figure: 2𝑅 (1) 11 (2) 14 𝑅 3 (3) 21 𝑅 (4) 8 𝑅 3

Q12.Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be: (1) 1: 4 (2) 4: 1 (3) 2: 1 (4) 1: 2 JEE Main 2023 (11 Apr Shift 1) JEE Main Previous Year Paper

Q12.The charge flowing in a conductor changes with time as 𝑄𝑡= 𝛼𝑡- 𝛽𝑡2 + 𝛾𝑡3, where 𝛼, 𝛽 and 𝛾 are constants. Minimum value of current is: (1) 3𝛽2 (2) 𝛾2 𝛼- 𝛼- 𝛾 3𝛽 (3) 𝛽- 𝛼2 (4) 𝛼- 𝛽2 3𝛾 3𝛾