Practice Questions

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.

Q47. In the given circuit the sliding contact is pulled outwards such that electric current in the circuit changes at the rate of 8 A/s. At an instant when R is 12Ω, the value of the current in the circuit will be ______ A.

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.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.In a series LCR circuit, a resistor of 300Ω, a capacitor of 25 nF and an inductor of 100 mH are used. For maximum current in the circuit, the angular frequency of the ac source is _____ ×104 radians s−1 .

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.

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.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 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

Q48.An electric dipole of dipole moment 6 × 10−6Cm is placed in uniform electric field of magnitude 106 V/m . Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ____ J.

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.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.The increase in pressure required to decrease the volume of a water sample by 0.2% is P × 105Nm−2 . Bulk modulus of water is 2.15 × 109Nm−2 . The value of P is … …

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.Two light beams fall on a transparent material block at point 1 and 2 with angle θ1 and θ2′ respectively, as shown in figure. After refraction, the beams intersect at point 3 which is exactly on the interface at other end of the block. Given : the distance between 1 and 2, d = 4√3 cm and θ1 = θ2 = cos−1 ( 2n1n2 ), where refractive index of the block n2 > refractive index of the outside medium n1 , then the thickness of the block is ________ cm.

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.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 .

Q48.The position vectors of two 1 kg particles, (A) and (B), are given by→rA = (α1t2^i + α2t^j + α3t^k)m , respectively; →rB = (β1t^i + β2t2^j + β3t^k)m (α1 = 1 m/s2, α2 = 3nm/s, α3 = 2 m/s, β1 = 2 m/s, β2 = −1 m/s2, β3 = 4pm/s), where t is time, n and p −→ are constants. At t = 1 s, VA = →VB and velocities →VA and →VB of the particles are orthogonal to each other. At t = 1 s, the magnitude of angular momentum of particle (A) with respect to the position of particle (B) is √Lkgm2 s−1 . The value of L is _______ .

Q49.Two cars P and Q are moving on a road in the same direction. Accleration of car P increases linearly with time whereas car Q moves with a constant accleration. Both cars cross each other at time t = 0, for the first time. The maximum possible number of crossing(s) (including the crossing at t = 0) is ________.

Q49.A tightly wound long solenoid carries a current of 1.5 A . An electron is executing uniform circular motion inside the solenoid with a time period of 75 ns . The number of turns per metre in the solenoid is … … -. [Take mass of electron me = 9 × 10−31 kg, charge of electron |qe| = 1.6 × 10−19C, μ0 = 4π × 10−7 N , 1 ns = 10−9 A2 s]

Q49.A tube of length 1 m is filled completely with an ideal liquid of mass 2 M , and closed at both ends. The tube is rotated uniformly in horizontal plane about one of its ends. If the force exerted by the liquid at the other end is F then angular velocity of the tube is in SI unit. The value of α is __________. √FαM

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. A conducting bar moves on two conducting rails as shown in the figure. A constant magnetic field B exists into the page. The bar starts to move from the vertex at time t = 0 with a constant velocity. If the induced EMF is E ∝tn , then value of n is _.