Practice Questions

Q1. A simple pendulum is being used to determine the value of gravitational acceleration g at a certain place. The length of the pendulum is 25.0 cm and a stopwatch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in g is: (1) 5.40% (2) 3.40% (3) 4.40% (4) 2.40%

Q5. A particle of mass m is dropped from a height h above the ground. At the same time another particle of the same mass is thrown vertically upwards from the ground with a speed of √2gh. If they collide head-on completely inelastically, the time taken for the combined mass to reach the ground, in units of is: √hg (1) √12 (2) √34 (3) 1 (4) 2 √32

Q5. In a reactor, 2 kg of 92U235 fuel is fully used up in 30 days. The energy released fission is 200 MeV . Given that the Avogadro number, N = 6. 023 × 1026 per kilo mole and 1 eV = 1. 6 × 10−19 J. The power output of the reactor is close to: JEE Main 2020 (02 Sep Shift 1) JEE Main Previous Year Paper (1) 35 MW (2) 60 MW (3) 125 MW (4) 54 MW

Q6. A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of 5.00 cm s−1 . Its kinetic energy is: (1) 8.75 × 10−4 J (2) 8.75 × 10−3 J (3) 6.25 × 10−4 J (4) 1.13 × 10−3 J

Q6. The mass density of a planet of radius R varies with the distance r from its centre as ρ(r) = ρ0(1 −r2R2 ) Then the gravitational field is maximum at: (1) (2) r = R R r = √34 (3) r = 1 R (4) R √3 r = √59

Q8. A calorimeter of water equivalent 20 g contains 180 g of water at 25°C. ′m′' grams of steam at 100°C is mixed in it till the temperature of the mixture is 31°C. The value of ′m′ is close to (Latent heat of water = 540 cal g−1 , specific heat of water = 1 cal g−1°C−1 ) (1) 2 (2) 4 (3) 3. 2 (4) 2. 6

Q8. A Carnot engine having an efficiency of 1 is being used as a refrigerator. If the work done on the refrigerator 10 is 10 J, the amount of heat absorbed from the reservoir at a lower temperature is (1) 99 J (2) 100 J (3) 1 J (4) 90 J JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper

Q10.A transverse wave travels on a taut steel wire with a velocity of v when tension in it is 2.06 × 104N. When the tension is changed to T, the velocity changed to 2v . The value of T is close to: (1) 2.50 × 104N (2) 5.15 × 103 N (3) 30.5 × 104 N (4) 10.2 × 102 N

Q13.A galvanometer having a coil resistance 100 Ω gives a full scale deflection when a current of 1mA is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter given full scale deflection for a potential difference of 10V? (1) 10kΩ (2) 8.9 kΩ (3) 7.9 kΩ (4) 9.9 kΩ

Q13.A beam of protons with speed 4 × 105 m s−1 enters a uniform magnetic field of 0. 3 T at an angle 60° to the magnetic field, the pitch of the resulting helical path of protons is close to : (Mass of the proton = 1. 67 × 10−27 kg, charge of the proton = 1. 69 × 10−19C) (1) 2 cm (2) 5 cm (3) 12 cm (4) 4 cm

Q15.A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate dB /dt = 0. 032 Ts−1. The induced current in the loopis close to (Resistivity of the metal wire is 1. 23 × 10−8 Ωm ) (1) 0.43 A (2) 0.61 A (3) 0.34 A (4) 0.53 A

Q21.A particle is moving along the x -axis with its coordinate with time t given by x(t) = 10 + 8t −3t2. Another particle is moving along the y -axis with its coordinate as a function of time given by y(t) = 5 −8t3. At t = 1 s, the speed of the second particle as measured in the frame of the first particle is given as √v. Then v(in m s−1) is ___________.

Q21.Starting at temperature 300K, one mole of an ideal diatomic gas (γ = 1.4) is first compressed adiabatically from volume V1 to V2 = V116 . It is then allowed to expand isobarically to volume 2V2 . If all the processes are the quasi-static then the final temperature of the gas (in oK ) is (to the nearest integer) ___________. →

Q21.A cricket ball of mass 0. 15 kg is thrown vertically up by a bowling machine so that it rises to a maximum height of 20 m after leaving the machine. If the part pushing the ball applies a constant force F on the ball applies a constant force F on the ball and moves horizontally a distance of 0. 2 m while launching the ball, the value of F(in N) is (g = 10 m s−2)

Q21.A block starts moving up an inclined plane of inclination 30° with an initial velocity of v0 . It comes back to its initial position with velocity v0 2 . The value of the coefficient of kinetic friction between the block and the inclined plane is close to 1 , The nearest integer to I is : 1000

Q21. ABC is a plane lamina of the shape of an equilateral triangle. D, E are mid-points of AB, AC and G is the centroid of the lamina. Moment of inertia of the lamina about an axis passing through G and perpendicular to the plane ABC is I0 . If part ADE is removed, the moment of inertia of the remaining part about the same axis is NI0 where N is an integer. Value of N is: 16

Q21.A ball is dropped from the top of a 100 m high tower on a planet. In the last 21 s before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in m s−2 ) near the surface on that planet is______

Q21.A particle (m = 1kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2m ). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1m ), the kinetic energy of the particle (in J ) is: (Figure drawn is schematic and not to scale; take g = 10ms−2 ) ______________.

Q21.The centre of mass of a solid hemisphere of radius 8 cm is x cm from the centre of the flat surface. Then value of x is

Q21.The distance x covered by a paritcle in one dimensional motion varies with time t as x2 = at2 + 2bt + c . If the acceleration of the particle depends on x as x−n , where n is an integer, the value of n is _________

Q21.The sum of two forces P and Q is R such that R = P . Find the angle between resultant of 2P and Q and Q , ________ JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper

Q21.A small block starts slipping down from a point B on an inclined plane AB, which is making an angle θ with the horizontal section BC is smooth and the remaining section CA is rough with a coefficient of friction μ. It is found that the block comes to rest as it reaches the bottom (point A) of the inclined plane. If BC = 2AC , the coefficient of friction is given by μ = k tanθ . The value of k is ....... JEE Main 2020 (02 Sep Shift 1) JEE Main Previous Year Paper

Q21.The density of a solid metal sphere is diameter. The maximum error in the density of the sphere is ( 100x )%. If the relative errors in measuring the mass and the diameter are 6. 0% and 1. 5% respectively, the value of x is −

Q21.A square shaped hole of side l = 2a is carved out at a distance d = a2 from the centre ' O ' of a uniform circular disk of radius a. If the distance of the centre of mass of the remaining portion from O is −ax , value of X (to the nearest integer) is :

Q21.The speed verses time graph for a particle is shown in the figure. The distance travelled (in m) by the particle during the time interval t = 0 to t = 5 s will be __________