Practice Questions

Q41.A light hollow cube of side length 10 cm and mass 10 g , is floating in water. It is pushed down and released to execute simple harmonic oscillations. The time period of oscillations is yπ × 10−2 s, where the value of y is (Acceleration due to gravity, g = 10 m/s2 , density of water = 103 kg/m3 ) 2025 (23 Jan Shift 1) JEE Main Previous Year Paper (1) 6 (2) 2 (3) 4 (4) 1

Q41.If a satellite orbiting the Earth is 9 times closer to the Earth than the Moon, what is the time period of rotation of the satellite? Given rotational time period of Moon = 27 days and gravitational attraction between the satellite and the moon is neglected. (1) 27 days (2) 1 day (3) 81 days (4) 3 days

Q45.A solid sphere of mass ' m ' and radius ' r ' is allowed to roll without slipping from the highest point of an inclined plane of length ' L ' and makes an angle 30∘ with the horizontal. The speed of the particle at the bottom of the plane is v1 . If the angle of inclination is increased to 45∘ while keeping L constant. Then the new speed of the sphere at the bottom of the plane is v2 . The ratio v21 : v22 is (1) 1 : √2 (2) 1 : √3 (3) 1 : 3 (4) 1 : 2 2025 (23 Jan Shift 1) JEE Main Previous Year Paper

Q46.The ratio of the power of a light source S1 to that the light source S2 is 2. S1 is emitting 2 × 1015 photons per second at 600 nm . If the wavelength of the source S2 is 300 nm , then the number of photons per second emitted by S2 is … … ×1014 . 2025 (24 Jan Shift 2) JEE Main Previous Year Paper

Q46.The magnetic field inside a 200 turns solenoid of radius 10 cm is 2.9 × 10−4Tesla. If the solenoid carries a current of 0.29 A , then the length of the solenoid is ________ πcm .

Q46.In a hydraulic lift, the surface area of the input piston is 6 cm2 and that of the output piston is 1500 cm2 . If 100 N force is applied to the input piston to raise the output piston by 20 cm, then the work done is _______ kJ. 2025 (29 Jan Shift 1) JEE Main Previous Year Paper

Q46.A proton is moving undeflected in a region of crossed electric and magnetic fields at a constant speed of 2 × 105 ms−1 . When the electric field is switched off, the proton moves along a circular path of radius 2 cm . The magnitude of electric field is x × 104 N/C. The value of x is _______ Take the mass of the proton = 1.6 × 10−27 kg.

Q46.A time varying potential difference is applied between the plates of a parallel plate capacitor of capacitance 2.5μ F. The dielectric constant of the medium between the capacitor plates is 1 . It produces an instantaneous displacement current of 0.25 mA in the intervening space between the capacitor plates, the magnitude of the rate of change of the potential difference will be _____ Vs−1 .

Q46.A current of 5A exists in a square loop of side 1 m . Then the magnitude of the magnetic field B at the centre √2 of the square loop will be p × 10−6 T. where, value of p is _____ . [ Take μ0 = 4π × 10−7TmA−1].

Q47.A parallel plate capacitor consisting of two circular plates of radius 10 cm is being charged by a constant current of 0.15 A . If the rate of change of potential difference between the plates is 7 × 108 V/s then the integer value of the distance between the parallel plates is ( Take, ϵ0 = 9 × 10−12 mF , π = 227 ) ________ μm . 2025 (29 Jan Shift 2) JEE Main Previous Year Paper

Q47.In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of [M aLbT c]. If b = −3, the value of c is ________

Q47.A square loop of sides a = 1 m is held normally in front of a point charge q = 1C. The flux of the electric 1 Nm2 field through the shaded region is , where the value of p is _____. 5 × p C ε0

Q47.The coordinates of a particle with respect to origin in a given reference frame is (1, 1, 1) meters. If a force of → F = ^i −^j + ^k acts on the particle, then the magnitude of torque (with respect to origin) in z-direction is ______.

Q47.Two soap bubbles of radius 2 cm and 4 cm , respectively, are in contact with each other. The radius of curvature of the common surface, in cm , is ______ . and

Q47.The value of current I in the electrical circuit as given below, when potential at A is equal to the potential at B, will be ____ A.

Q47. A string of length L is fixed at one end and carries a mass of M at the other end. The mass makes ( π3 ) rotations per second about the vertical axis passing through end of the string as shown. The tension in the string is … … ML.

Q47.The net current flowing in the given circuit is_______ A.

Q48.An air bubble of radius 1.0 mm is observed at a depth of 20 cm below the free surface of a liquid having surface tension 0.095 J/m2 and density 103 kg/m3 . The difference between pressure inside the bubble and atmospheric pressure is _____ N/m2 . (Take g = 10 m/s2 )

Q48.Two planets, A and B are orbiting a common star in circular orbits of radii RA and RB , respectively, with RB = 2RA . The planet B is 4√2 times more massive than planet A . The ratio ( LBLA ) of angular momentum (LB) of planet B to that of planet A (LA) is closest to integer ________.

Q48.A tiny metallic rectangular sheet has length and breadth of 5 mm and 2.5 mm , respectively. Using a specially designed screw gauge which has pitch of 0.75 mm and 15 divisions in the circular scale, you are asked to find the area of the sheet. In this measurement, the maximum fractional error will be x where x is _________. 100

Q48.The temperature of 1 mole of an ideal monoatomic gas is increased by 50∘C at constant pressure. The total heat added and change in internal energy are E1 and E2 , respectively. If E1 = x9 then the value of x is _____ E2

Q48.A parallel plate capacitor of area A = 16 cm2 and separation between the plates 10 cm , is charged by a DC current. Consider a hypothetical plane surface of area A0 = 3.2 cm2 inside the capacitor and parallel to the plates. At an instant, the current through the circuit is 6A. At the same instant the displacement current through A0 is ________ mA .

Q49.Three conductors of same length having thermal conductivity k1, k2 and k3 are connected as shown in figure. Area of cross sections of 1st and 2nd conductor are same and for 3rd conductor it is double of the 1st conductor. The temperatures are given in the figure. In steady state condition, the value of θ is _______ ∘C. (Given : k1 = 60Js−1 m−1 K−1, k2 = 120Js−1 m−1 K−1, k3 = 135Js−1 m−1 K−1 ) ∣ ∣∣ 2025 (22 Jan Shift 1) JEE Main Previous Year Paper

Q49.A satellite of mass M is revolving around earth in a circular orbit at a height of R from earth surface. The 2 3 angular momentum of the satellite is . The value of x is ______ , where M and R are the mass and M√GMRx radius of earth, respectively. ( G is the gravitational constant)

Q49.An ideal gas initially at 0∘C temperature, is compressed suddenly to one fourth of its volume. If the ratio of specific heat at constant pressure to that at constant volume is 3/2, the change in temperature due to the thermodynamic process is _____ K.