Practice Questions

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.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 ________

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.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 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 _______ .

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.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.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.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.

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.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 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 _.

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.

Q49.Two iron solid discs of negligible thickness have radii R1 and R2 and moment of intertia I1 and I2 , respectively. For R2 = 2R1 , the ratio of I1 and I2 would be 1/x, where x = ________ -

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.The least count of a screw guage is 0.01 mm . If the pitch is increased by 75% and number of divisions on the circular scale is reduced by 50% , the new least count will be _____ ×10−3 mm

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)

Q50.A physical quantity Q is related to four observables a, b, c, d as follows : Q = ab4cd where, a = (60 ± 3)Pa; b = (20 ± 0.1)m; c = (40 ± 0.2)Nsm−2 and d = (50 ± 0.1)m , then the percentage error in Q is x , where x = ________ . 1000

Q50.A wire of resistance 9Ω is bent to form an equilateral triangle. Then the equivalent resistance across any two vertices will be _____ ohm.

Q50.Acceleration due to gravity on the surface of earth is ' g '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is … … g.

Q50.Two long parallel wires X and Y , separated by a distance of 6 cm , carry currents of 5A and 4A, respectively, in opposite directions as shown in the figure. Magnitude of the resultant magnetic field at point P at a distance 2025 (22 Jan Shift 2) JEE Main Previous Year Paper of 4 cm from wire Y is x × 10−5 T. The value of x is__________ . Take permeability of free space as μ0 = 4π × 10−7SI units.

Q50.The maximum speed of a boat in still water is 27 km/h. Now this boat is moving downstream in a river flowing at 9 km/h. A man in the boat throws a ball vertically upwards with speed of 10 m/s. Range of the ball as observed by an observer at rest on the river bank, is _______ cm. (Take g = 10 m/s2 )