Practice Questions

Q12.A mass m = 1.0 kg is put on a flat pan attached to a vertical spring fixed on the ground. The mass of the spring and the pan is negligible. When pressed slightly and released, the mass executes simple harmonic motion. The spring constant is 500 N/m. What is the amplitude A of the motion, so that the mass m tends to get detached from the pan ? (Take g = 10 m/s2 ). The spring is stiff enough so that it does not get distorted during the motion. JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper (1) A > 2.0 cm (2) A = 2.0 cm (3) A < 2.0 cm (4) A = 1.5 cm

Q12.This question has Statement-1 and Statement-2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: The internal energy of a perfect gas is entirely kinetic and depends only on absolute temperature of the gas and not on its pressure or volume. Statement 2: A perfect gas is heated keeping pressure constant and later at constant volume. For the same amount of heat the temperature of the gas at constant pressure is lower than that at constant volume. (1) Statement-1 is true, Statement- 2 is true and (2) Statement-1 is true, Statement-2 is false. Statement −2 is the correct explanation of Statement-1. (3) Statement-1 is true, Statement-2 is true but (4) Statement-1 is false, Statement-2 is true. Statement-2 is not the correct explanation of Statement-1.

Q12.A sonometer wire of length 1 .5 m is made of steel. The tension in it produces an elastic strain of 1%. What is the fundamental frequency of steel if density and elasticity of steel are 7 .7 ×103 kg m−3 and 2 .2 ×1011 N m−2 respectively? (1) 200 .5 Hz (2) 770 Hz (3) 188 .5 Hz (4) 178 .2 Hz

Q13.The surface charge density of a thin charged disc of radius R is σ. The value of the electric field at the centre of the disc is σ . With respect to the field at the centre, the electric field along the axis at a distance R from 2∈0 the centre of the disc: (1) reduces by 70.7% (2) reduces by 29.3% (3) reduces by 9.7% (4) reduces by 14.6%

Q13.A charge Q is uniformly distributed over a long rod AB of length L as shown in the figure. The electric potential at the point O lying at a distance L from the end A is : (1) Q (2) Q ln 2 4π∈0L ln 2 4π∈0L (3) Q (4) 3Q 8π∈0L 4π∈0L

Q13.An engine approaches a hill with a constant speed. When it is at a distance of 0.9 km, it blows a whistle whose echo is heard by the driver after 5 seconds. If the speed of sound in air is 330 m/s , then the speed of the engine is : (1) 32 m/s (2) 27.5 m/s (3) 60 m/s (4) 30 m/s

Q13.Bob of a simple pendulum of length l is made of iron. The pendulum is oscillating over a horizontal coil carrying direct current. If the time period of the pendulum is T then : JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper (1) and damping is smaller than in air alone. T < 2π√lg and damping is larger than in air alone. (2) T = 2π√lg and damping is smaller than in air alone. (3) T > 2π√lg (4) and damping is larger than in air alone. T < 2π√lg

Q14.A sonometer wire of length 114 cm is fixed at both the ends. Where should the two bridges be placed so as to divide the wire into three segments whose fundamental frequencies are in the ratio 1 : 3 : 4 ? (1) At 36 cm and 84 cm from one end (2) At 24 cm and 72 cm from one end (3) At 48 cm and 96 cm from one end (4) At 72 cm and 96 cm from one end

Q14.The gravitational field in a region is given by: →E = (5N/kg)^i + (12N/kg)^j If the potential at the origin is taken to be zero, then the ratio of the potential at the points (12 m, 0) and (0, 5 m) is : (1) Zero (2) 1 (3) 144 (4) 25 25 144

Q14.Two point dipoles of dipole moment →p1 and →p2 are at a distance x from each other and →p1||→p2 . The force between the dipoles is : (1) 1 4p1p2 (2) 1 3p1p2 4πε0 x4 4πε0 x3 (3) 1 6p1p2 (4) 1 8p1p2 4πε0 x4 4πε0 x4

Q14.In an LCR circuit as shown below both switches are open initially. Now switch S1 is closed, S2 kept open. ( q is charge on the capacitor and τ = RC is capacitive time constant). Which of the following statement is correct? (1) At t = 2τ, q = CV (1 −e−2) (2) At t = τ2 , q = CV (1 −e−1) (3) Work done by the battery is half of the energy (4) At t = τ, q = CV/2 dissipated in the resistor

Q14.A point charge of magnitude +1μC is fixed at (0 , 0, 0). An isolated uncharged spherical conductor, is fixed with its center at (4, 0, 0). The potential and the induced electric field at the centre of the sphere is : (1) 1.8 × 105 V and −5.625 × 106 V/m (2) 0 V and 0 V/m (3) 2.25 × 105 V and −5.625 × 106 V/m (4) 2.25 × 105 V and 0 V/m

Q15.Consider a finite insulated, uncharged conductor placed near a finite positively charged conductor. The uncharged body must have a potential : (1) less than the charged conductor and more than at infinity. (2) more than the charged conductor and less than at infinity. (3) more than the charged conductor and more than at infinity. (4) less than the charged conductor and less than at infinity.

Q15.Two small equal point charges of magnitude q are suspended from a common point on the ceiling by insulating mass less strings of equal lengths. They come to equilibrium with each string making angle θ from the vertical. If the mass of each charge is m, then the electrostatic potential at the centre of line joining them will be 1 = ( 4π ∈0 k). (1) 2√kmg tan θ (2) √kmg tan θ (3) 4√kmg/ tan θ (4) 4√kmg/ tan θ

Q15.Two capacitors C1 and C2 are charged to 120 V and 200 V respectively. It is found that by connecting them together the potential on each one can be made zero. Then: (1) 3C1 + 5C2 = 0 (2) 9C1 = 4C2 (3) 5C1 = 3C2 (4) 3C1 = 5C2 JEE Main 2013 (07 Apr) JEE Main Previous Year Paper

Q15.A parallel plate capacitor having a separation between the plates d, plate area A and material with dielectric constant K has capacitance C0 . Now one-third of the material is replaced by another material with dielectric constant 2 K, so that effectively there are two capacitors one with area 31 A , dielectric constant 2 K and another with area 2 3 A and dielectric constant K. If the capacitance of this new capacitor is C then C0C is (1) 1 (2) 34 (3) 2 (4) 1 3 3 JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper

Q15.Two balls of same mass and carrying equal charge are hung from a fixed support of length l. At electrostatic equilibrium, assuming that angles made by each thread is small, the separation, x between the balls is proportional to : (1) l (2) l2 (3) l2/3 (4) l1/3

Q16.A liquid drop having 6 excess electrons is kept stationary under a uniform electric field of 25.5 kVm−1 . The density of liquid is 1.26 × 103 kg m−3 . The radius of the drop is (neglect buoyancy). (1) 4.3 × 10−7 m (2) 7.8 × 10−7 m (3) 0.078 × 10−7 m (4) 3.4 × 10−7 m

Q16.Six equal resistances are connected between points P, Q and R as shown in figure. Then net resistance will be maximum between : (1) P and R (2) P and Q (3) Q and R (4) Any two points

Q16.In a metre bridge experiment null point is obtained at 40 cm from one end of the wire when resistance X is balanced against another resistance Y . If X < Y , then the new position of the null point from the same end, if one decides to balance a resistance of 3X against Y , will be close to : (1) 80 cm (2) 75 cm (3) 67 cm (4) 50 cm

Q16.The supply voltage to a room is 120 V . The resistance of the lead wires is 6 Ω. A 60 W bulb is already switched on. What is the decrease of voltage across the bulb, when a 240 W heater is switched on in parallel to the bulb? (1) 13 .3 V (2) 10. 4 V (3) zero V (4) 2 .9 V

Q17.The earth's magnetic field lines resemble that of a dipole at the centre of the earth. If the magnetic moment of this dipole is close to 8 × 1022Am2 , the value of earth's magnetic field near the equator is close to (radius of the earth = 6.4 × 106 m) (1) 0.6 Gauss (2) 1.2 Gauss (3) 1.8 Gauss (4) 0.32 Gauss

Q17.A parallel plate capacitor of area 60 cm2 and separation 3 mm is charged initially to 90μC. If the medium between the plate gets slightly conducting and the plate loses the charge initially at the rate of 2.5 × 10−8C/s, then what is the magnetic field between the plates ? (1) 2.5 × 10−8 T (2) 2.0 × 10−7 T (3) 1.63 × 10−11 T (4) Zero

Q17.A dc source of emf E1 = 100 V and internal resistance r = 0.5Ω, a storage battery of emf E2 = 90 V and an external resistance R are connected as shown in figure. For what value of R no current will pass through the JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper battery? (1) 5.5Ω (2) 3.5Ω (3) 4.5Ω (4) 2.5Ω

Q18.A shunt of resistance 1 Ω is connected across a galvanometer of 120 Ω resistance. A current of 5.5 ampere gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly : (1) 5.5 ampere (2) 0.5 ampere (3) 0.004 ampere (4) 0.045 ampere