Practice Questions

Q23.A rod of mass M and length L is lying on a horizontal frictionless surface. A particle of mass m travelling along the surface hits at one end of the rod with a velocity u in a direction perpendicular to the rod. The collision is completely elastic. After collision, particle comes to rest. The ratio of masses ( Mm ) is x1 . The value of x will be

Q23.Consider a badminton racket with length scales as shown in the figure. JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper If the mass of the linear and circular portions of the badminton racket are same ( M ) and the mass of the threads are negligible, the moment of inertia of the racket about an axis perpendicular to the handle and in the plane of the ring at, r distance from the end A of the handle will be ______ Mr2 . 2

Q24.A ball of mass 10 kg moving with a velocity 10√3 m s−1 along X -axis, hits another ball of mass 20 kg which is at rest. After the collision, the first ball comes to rest and the second one disintegrates into two equal pieces. One of the pieces starts moving along Y -axis at a speed of 10 m s−1 . The second piece starts moving at a speed of 20 m s−1 at an angle θ (degree) with respect to the X -axis. The configuration of pieces after the collision is shown in the figure. The value of θ to the nearest integer is _________.

Q24.Consider an electrical circuit containing a two way switch S. Initially S is open and then T1 is connected to T2. As the current in R = 6 Ω attains a maximum value of steady-state level, T1 is disconnected from T2 and JEE Main 2021 (27 Jul Shift 1) JEE Main Previous Year Paper immediately connected to T3. Potential drop across r = 3 Ω resistor immediately after T1 is connected to T3 is ______V. (Round off to the Nearest Integer)

Q24.A ball of mass 10 kg moving with a velocity 10√3 m s−1 along the x -axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while the second ball disintegrates into two equal pieces. One piece starts moving along y -axis with a speed of 10 m s−1. The second piece starts moving at an angle of 30° with respect to the x -axis. The velocity of the ball moving at 30° with x -axis is x m s−1. The configuration of pieces after the collision is shown in the figure below. The value of x to the nearest integer is JEE Main 2021 (18 Mar Shift 1) JEE Main Previous Year Paper

Q25.A particle of mass 1 mg and charge 𝑞 is lying at the mid-point of two stationary particles kept at a distance 2 m when each is carrying same charge 𝑞. If the free charged particle is displaced from its equilibrium position through distance 𝑥 𝑥< < 1 m. The particle executes SHM. Its angular frequency of oscillation will be _______ × 105 rad s-1 (if 𝑞2 = 10𝐶2)

Q25.If the maximum value of accelerating potential provided by a radio frequency oscillator is 12 kV . The number of revolution made by a proton in a cyclotron to achieve one sixth of the speed of light is: [mp = 1. 67 × 10−27 kg, e = 1. 6 × 10−19 C, Speed of light = 3 × 108 m s−1]

Q26.A light beam of wavelength 500 nm is incident on a metal having work function of 1. 25 eV , placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into a circular arc of radius 30 cm. The value of B is ________ ×10−7 T. Given hc = 20 × 10−26 J m, the mass of the electron = 9 × 10−31 kg. JEE Main 2021 (25 Jul Shift 2) JEE Main Previous Year Paper

Q27.A closed organ pipe of length L and an open organ pipe contain gases of densities ρ1 and ρ2 respectively. The compressibility of gases are equal in both the pipes. Both the pipes are vibrating in their first overtone with same frequency. The length of the open pipe is x , where x is _______. 3 L√ρ1ρ2 (Round off to the Nearest Integer)

Q27.Two short magnetic dipoles m1 and m2 each having magnetic moment of 1 A m2 are placed at point O and P respectively. The distance between OP is 1 m . The torque experienced by the magnetic dipole m2 due to the presence of m1 is ________ × 10−7N m

Q28.A radioactive sample has an average life of 30 ms and is decaying. A capacitor of capacitance 200 μF is first charged and later connected with resistor R. If the ratio of the charge on the capacitor to the activity of the radioactive sample is fixed with respect to time then the value of R should be _______Ω.

Q28.Two stream of photons, possessing energies equal to twice and ten times the work function of metal are incident on the metal surface successively. The value of ratio of maximum velocities of the photoelectrons emitted in the two respective cases is x : 3 The value of x is

Q28.An object is placed at a distance of 12 cm from a convex lens. A convex mirror of focal length 15 cm is placed on another side of the lens at 8 cm as shown in the figure. The image of the object coincides with the object. When the convex mirror is removed, a real and inverted image is formed at a position. The distance of the image from the object will be ___ cm JEE Main 2021 (26 Aug Shift 2) JEE Main Previous Year Paper

Q28.A circular conducting coil of radius 1 m is being heated by the change of magnetic field →𝐵 passing perpendicular to the plane in which the coil is laid. The resistance of the coil is 2 μΩ. The magnetic field is slowly switched off such that its magnitude changes in time as 4 𝑡 𝐵= 𝜋× 10-3 𝑇1 - 100 The energy dissipated by the coil before the magnetic field is switched off completely is 𝐸= ______mJ.

Q28.Seawater at a frequency f = 9 × 102 Hz , has permittivity ε = 80ε0 and resistivity ρ = 0. 25 Ω m . Imagine a parallel plate capacitor is immersed in seawater and is driven by an alternating voltage source V (t) = V0 sin(2πft). Then the conduction current density becomes 10x times the displacement current density after time t = 8001 s. The value of x is _______ (Given : 1 = 9 × 109 N m2 4πε0 C−2)

Q29.The Kα X-ray of molybdenum has wavelength 0. 071 nm. If the energy of a molybdenum atom with a K electron knocked out is 27. 5 keV, the energy of this atom when an L electron is knocked out will be keV. (Round off to the nearest integer ) [h = 4. 14 × 10−15 eV s, c = 3 × 108 m s−1]

Q29.An object viewed from a near point distance of 25 cm, using a microscopic lens with magnification 6, gives an unresolved image. A resolved image is observed at infinite distance with a total magnification double the earlier using an eyepiece along with the given lens and a tube of length 0. 6 m, if the focal length of the eyepiece is equal to ____ cm.

Q29.Two satellites revolve around a planet in coplanar circular orbits in anticlockwise direction. Their period of revolutions are 1 hour and 8 hours respectively. The radius of the orbit of nearer satellite is 2 × 103 km . The angular speed of the farther satellite as observed from the nearer satellite at the instant when both the satellites are closest is 𝜋 h-1, where 𝑥 is _______ . 𝑥rad

Q30.A particle of mass m moves in a circular orbit in a central potential field U(r) = U0r4. If Bohr's quantization α , where α is _______ . conditions are applied, radii of possible orbitals rn vary with n 1

Q30.A deviation of 2° is produced in the yellow ray when prism of crown and flint glass are achromatically combined. Taking dispersive powers of crown and flint glass are 0. 02 and 0. 03 respectively and refractive JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper index for yellow light for these glasses are 1. 5 and 1. 6 respectively. The refracting angles for crown glass prism will be ________ ° (in degree) (Round off to the Nearest Integer)

Q31.Complete combustion of 1. 80 g of an oxygen containing compound (CxHyOz) gave 2. 64 g of CO2 and 1. 08 g of H2O. The percentage of oxygen in the organic compound is : (1) 53. 33 (2) 50. 33 (3) 51. 63 (4) 63. 53

Q2. A block of mass m = 1 kg slides with velocity v = 6 m s−1 on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about O and swings as a result of the collision making angle θ before momentarily coming to rest. if the rod has mass M = 2 kg, and length ℓ= 1 m, the value of θ is approximately (take g = 10 m s−2) (1) 63° (2) 55° (3) 69° (4) 49°

Q3. A bead of mass m stays at point P(a, b) on a wire bent in the shape of a parabola y = 4Cx2 and rotating with angular speed ω (see figure). The value of ω is (neglect friction) (1) 2√2gC (2) √2gC (3) √2gCab (4) √2gC

Q3. Particle A of mass m1 moving with velocity (√3ˆi +ˆj) ms−1 collides with another particle which is at rest initially. Let →v1 and →v2 be the velocities of particles A and B after collision respectively. If + and →v2 is : m1 = 2m2 and after collision →v1 −(ˆi √3ˆj) ms−1 , the angle between →v1 (1) 15° (2) 60° (3) −45° (4) 105°

Q3. A satellite is moving in a low nearly circular orbit around the earth. Its radius is roughly equal to that of the earth's radius Re. By firing rockets attached to it, its speed is instantaneously increased in the direction of its motion so that it become times larger. Due to this the farthest distance from the centre of the earth that the √32 satellite reaches is R. Value of R is : (1) 4Re (2) 2. 5Re (3) 3Re (4) 2Re