Practice Questions

Q9. A hydraulic automobile lift is designed to lift vehicles of mass 5000 kg. The area of cross section of the cylinder carrying load is 250 cm2 . The maximum pressure the smaller piston would have to bear is [Assume g = 10 m s−2 ] (1) 20 × 106 Pa (2) 2 × 105 Pa (3) 200 × 106 Pa (4) 2 × 106 Pa

Q9. Match List I with List II: List I List II (A)3 Translational degrees of freedom (I) Monoatomic gases (B) 3 Translational, 2 rotational degrees of freedoms (II) Polyatomic gases 3 Translational, 2 rotational and 1 vibrational degrees Rigid diatomic (C) (III) of freedom gases (D)3 Translational, 3 rotational and more than one (IV)Nonrigid diatomic vibrational degrees of freedom gases Choose the correct answer from the options given below: (1) A - I, B - III, C - IV, D - II (2) A - IV, B - III, C - II, D - I (3) A - IV, B - II, C - I, D - III (4) A - I, B - IV, C - III, D - II 𝐴

Q9. A force is applied to a steel wire A , rigidly clamped at one end. As a result elongation in the wire is 0. 2 mm. If same force is applied to another steel wire B of double the length and a diameter 2. 4 times that of the wire A, the elongation in the wire B will be (wires having uniform circular cross sections) (1) 6. 06 × 10–2 mm (2) 2. 77 × 10–2 mm (3) 3. 0 × 10–2 mm (4) 6. 9 × 10–2 mm

Q9. The weight of a body on the earth is 400 N. Then weight of the body when taken to a depth half of the radius of the earth will be: (1) 200 N (2) Zero (3) 100 N (4) 300 N

Q10.The pressure ( 𝑃) and temperature ( 𝑇) relationship of an ideal gas obeys the equation 𝑃𝑇2 = constant. The volume expansion coefficient of the gas will be : 3 (1) 3𝑇2 (2) 𝑇2 3 3 (3) (4) 𝑇3 𝑇

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.A particle executes S.H.M. of amplitude 𝐴 along 𝑥-axis. At 𝑡= 0, the position of the particle is 𝑥= and it 2 moves along positive 𝑥-axis. The displacement of particle in time 𝑡 is 𝑥= 𝐴 sin𝜔𝑡 + 𝛿, then the value 𝛿 will be (1) 𝜋 (2) 𝜋 2 6 𝜋 𝜋 (3) (4) 3 4

Q10.A fully loaded boeing aircraft has a mass of 5. 4 × 105 kg. Its total wing area is 500 m2 . It is in level flight with a speed of 1080 km h−1 . If the density of air ρ is 1. 2 kg m–3 , the fractional increase in the speed of the air on the upper surface of the wing relative to the lower surface in percentage will be ( g = 10 m s−2 ) (1) 16 (2) 6 (3) 8 (4) 10

Q10.The Young's modulus of a steel wire of length 6 m and cross-sectional area 3 mm2 , is 2 × 1111 N/m2 . The wire is suspended from its support on a given planet. A block of mass 4 kg is attached to the free end of the JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper wire. The acceleration due to gravity on the planet is 1 of its value on the earth. The elongation of wire is 4 (Take g on the earth = 10 m/s2 ): (1) 1 cm (2) 1 mm (3) 0. 1 mm (4) 0. 1 cm

Q10.The number of air molecules per cm3 is increased from 3 × 1019 to 12 × 1019 . The ratio of collision frequency of air molecules before and after the increase in number respectively is : (1) 0 . 75 (2) 1 . 25 (3) 0 . 50 (4) 0 . 25

Q10.A particle executes SHM of amplitude 𝐴. The distance from the mean position when its kinetic energy becomes equal to its potential energy is: (1) 1 (2) 2𝐴 √2𝐴 (3) √2𝐴 (4) 12𝐴

Q10.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion (A) : Steel is used in the construction of buildings and bridges. Reason (R) : Steel is more elastic and its elastic limit is high. In the light of above statements, choose the most appropriate answer from the options given below (1) Both A and R are correct and R is the correct (2) Both A and R are correct but R is NOT the explanation of A correct explanation of A (3) A is correct but R is not correct (4) A is not correct but R is correct

Q10.A steel wire with mass per unit length 7 . 0 × 10 – 3 kg m – 1 is under tension of 70 N. The speed of transverse waves in the wire will be: (1) 200π m s-1 (2) 100 m s-1 (3) 10 m s-1 (4) 50 m s-1

Q10.In a linear Simple Harmonic Motion (SHM) (A) Restoring force is directly proportional to the displacement. (B) The acceleration and displacement are opposite in direction. (C) The velocity is maximum at mean position. (D) The acceleration is minimum at extreme points. Choose the correct answer from the options given below: (1) (C) and (D) only (2) (A), (C) and (D) only (3) (A), (B) and (C) only (4) (A), (B) and (D) only

Q10.The distance between two plates of a capacitor is 𝑑 and its capacitance is 𝐶1, when air is the medium between 2𝑑 the plates. If a metal sheet of thickness and of the same area as plate is introduced between the plates, the 3 𝐶2 capacitance of the capacitor becomes 𝐶2 . The ratio is 𝐶1 (1) 3 : 1 (2) 2 : 1 (3) 4 : 1 (4) 1 : 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.The equivalent capacitance of the combination shown is (1) 2 C (2) 5 C 3 C (3) (4) 4 C 2

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.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

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.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.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.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.The electric field due to a short electric dipole at a large distance (r) from center of dipole on the equatorial plane varies with distance as : (1) r (2) 1 r2 (3) 1 (4) 1r r3

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)