Practice Questions

Q26.Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of 37° with each other. When suspended in a liquid of density 0 . 7 g cm-3, the angle remains same. If density of material 3 of the sphere is 1 . 4 g cm-3, the dielectric constant of the liquid is _____ tan37° = 4

Q26.Twelve wires each having resistance 2Ω are joined to form a cube. A battery of 6 V emf is joined across point a and c. The voltage difference between e and f is ______V.

Q26.A heater is designed to operate with a power of 1000 W in a 100 V line. It is connected in combination with a resistance of 10Ω and a resistance R, to a 100 V mains as shown in figure. For the heater to operate at 62.5 W, the value of R should be _____ Ω.

Q27.A square loop of edge length 2 m carrying current of 2 A is placed with its edges parallel to the x y axis. A magnetic field is passing through the x −y plane and expressed as →B = B0(1 + 4x)^k, where B0 = 5 T. The net magnetic force experienced by the loop is _______ N .

Q28.A small square loop of wire of side 𝑙 is placed inside a large square loop of wire of side 𝐿𝐿= 𝑙2. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is √𝑥× 10-7 H, where 𝑥= ______.

Q28.A rectangular loop of sides 12 cm and 5 cm, with its sides parallel to the 𝑥-axis and 𝑦-axis respectively moves with a velocity of 5 cm s-1 in the positive 𝑥 axis direction, in a space containing a variable magnetic field in the positive 𝑧 direction. The field has a gradient of 10-3 T cm-1 along the negative 𝑥 direction and it is decreasing with time at the rate of 10-3 T s-1 . If the resistance of the loop is 6 m𝛺, the power dissipated by the loop as heat is ______ × 10-9 W .

Q28.An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of 20μF is _____V.

Q28.A square loop PQRS having 10 turns, area 3.6 × 10−3 m2 and resistance 100Ω is slowly and uniformly being pulled out of a uniform magnetic field of magnitude B = 0.5 T as shown. Work done in pulling the loop out of JEE Main 2024 (08 Apr Shift 1) JEE Main Previous Year Paper the field in 1.0 s is ______ ×10−6 J.

Q29.Two slits are 1 mm apart and the screen is located 1 m away from the slits. A light of wavelength 500 nm is used. The width of each slit to obtain 10 maxima of the double slit pattern within the central maximum of the JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper single slit pattern is _____ ×10−4 m

Q30.When a hydrogen atom going from n = 2 to n = 1 emits a photon, its recoil speed is x5 m s−1 . Where x = _______. (Use: mass of hydrogen atom = 1. 6 × 10−27 kg , charge of electron e = 1. 6 × 10−19 C)

Q30.A star has 100% helium composition. It starts to convert three 4He into one 12C via triple alpha process as 4He + 4He + 4He →12C + Q. The mass of the star is 2.0 × 1032 kg and it generates energy at the rate of 5.808 × 1030 W. The rate of converting these 4He to 12C is n × 1042 s−1 , where n is _________ [ Take, mass of 4He = 4.0026u, mass of 12C = 12u ]

Q30.A hydrogen atom changes its state from n = 3 to n = 2. Due to recoil, the percentage change in the wave length of emitted light is approximately 1 × 10−n . The value of n is_____. [Given Rhc = 13.6eV, hc = 1242eVnm, h = 6.6 × 10−34 J s mass of the hydrogenatom = 1.6 × 10−27 kg ] JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

Q4. A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripetal acceleration are equal. The time taken by the car to complete first quarter of revolution, if it is 2 ) s . The value of t is ______. moving with an initial speed of 54 km h−1 is t(1–e– π

Q4. A small particle of mass m moves in such a way that its potential energy U = 12 mω2r2 where ω is constant and r is the distance of the particle from origin. Assuming Bohr’s quantization of momentum and circular orbit, the radius of nth orbit will be proportional to (1) √n (2) n1 (3) n2 (4) n

Q5. A ball of mass 200 g rests on a vertical post of height 20 m. A bullet of mass 10 g, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance 30 m and the bullet at a distance of 120 m from the foot of the post. The value of initial velocity of the bullet will be (if 𝑔= 10 m s-2) : (1) 120 m s-1 (2) 60 m s-1 (3) 400 m s-1 (4) 360 m s-1 𝐾

Q6. A body of mass 2 kg is initially at rest. It starts moving unidirectionally under the influence of a source of constant power P . Its displacement in 4 s is 31 α2√P m. The value of α will be ______. JEE Main 2023 (30 Jan Shift 2) JEE Main Previous Year Paper

Q7. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : A spherical body of radius ( 5 ± 0 . 1 ) mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of its terminal velocity is 4%. Reason R : The terminal velocity of the spherical body falling through the liquid is inversely proportional to its radius. In the light of the above statements, choose the correct answer from the options given below (1) Both A and R are true and R is the correct (2) Both A and R are true but R is NOT the correct explanation of A explanation of A (3) A is true but R is false (4) A is false but R is true

Q7. Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0. 5 cm respectively. The densities of materials are in the ratio 3 : 5 . The moment of inertia of these discs respectively about their diameters will be in the ratio of x . The value of x is ______. 6

Q8. A uniform disc of mass 0. 5 kg and radius r is projected with velocity 18 m s−1 at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s. After 2 s it acquires a purely rolling motion (see figure). The total kinetic energy of the disc after 2 s will be ______ J. (given, coefficient of friction is 0. 3 and g = 10 m s−2 ).

Q11.A body cools from 80oC to 60o in 5 minutes. The temperature for the surrounding is 20oC. The time it takes to cool from 60oC to 40oC is (1) 450 s (2) 420 s (3) 500 s (4) 253 s

Q12.Two long straight wires 𝑃 and 𝑄 carrying equal current 10 A each were kept parallel to each other at 5 cm distance. Magnitude of magnetic force experienced by 10 cm length of wire 𝑃 is 𝐹1. If distance between wires is halved and currents on them are doubled, force 𝐹2 on 10 cm length of wire 𝑃 will be: (1) 8𝐹1 (2) 10 𝐹1 𝐹1 𝐹1 (3) (4) 8 10

Q14.A wire of density 8 × 103 kg m−3 is stretched between two clamps 0. 5 m apart. The extension developed in the wire is 3. 2 × 10−4 m. If Y = 8 × 1010 N m−2 , the fundamental frequency of vibration in the wire will be _____ Hz

Q15.A dipole comprises of two charged particles of identical magnitude q and opposite in nature. The mass m of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated → by a distance l . If the dipole is placed in a uniform electric field E ; in such a way that dipole axis makes a JEE Main 2023 (06 Apr Shift 2) JEE Main Previous Year Paper → very small angle with the electric field, E . The angular frequency of the oscillations of the dipole when released is given by: (1) √3qE2ml (2) √8qEml (3) √4qEml (4) √8qE3ml

Q15.In a cuboid of dimension 2L × 2L × L , a charge q is placed at the centre of the surface S having area of 4L2 . The flux through the opposite surface to S is given by (1) q (2) q 12∈0 3∈0 (3) q (4) q 2∈0 6∈0

Q16.Two parallel plate capacitors C1 and C2 each having capacitance of 10 μF are individually charged by a 100 V D.C. source. Capacitor C1 is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor C2 is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor C1 is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be _____ V . (Assuming Dielectric constant = 10 )