Practice Questions

Q1. The period of oscillation of a simple pendulum is T = 2π√lg 1 mm accuracy and time for 100 oscillations of the pendulum is found to be 90 s using a wristwatch of 1 s resolution. The accuracy in the determination of g is (1) 5% (2) 4% (3) 3% (4) 1%

Q2. A beaker contains a fluid of density ρ kg , specific heat S kgoCJ and viscosity η . The beaker is filled up to height m3 ˙Q h. To estimate the rate of heat transfer per unit area ( A ) by convection when beaker is put on a hot plate, a Δθ ( inoC ) is the difference in the student proposes that it should depend on η , ( SΔθh ) and ( ρg1 ) when ˙Q temperature between the bottom and top of the fluid. In that situation the correct option for ( A ) is: (1) ( SΔθh )η (2) η( SΔθh )( ρ1g ) ηh (3) ( SΔθηh )( ρg1 ) (4) SΔθ

Q3. If electronic charge e, electron mass m, speed of light in vacuum c and Planck's constant h are taken as fundamental quantities, the permeability of vacuum μ0 can be expressed in units of: (1) ( mc2he2 ) (2) ( me2h ) (3) ( me2hc ) (4) ( ce2h )

Q3. A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from its equilibrium position and released from rest. After approaching half the distance ( x2 ) from the equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with velocity 3 m s−1 . The total initial energy of the spring is: (1) 0 .6 J (2) 0 .8 J (3) 1 .5 J (4) 0 .3 J

Q3. Given in the figure are two blocks A and B of weight 20 N and 100 N , respectively. These are being pressed against a wall by a force F and kept in equilibrium as shown. If the coefficient of friction between the blocks is 0. 1 and between block B and the wall is 0. 15 , the frictional force applied by the wall on block B is: (1) 150 N (2) 100 N (3) 80 N (4) 120 N

Q4. From the top of a 64 metres high tower, a stone is thrown upwards vertically with the velocity of 48 m/s. The greatest height (in metres) attained by the stone, assuming the value of the gravitational acceleration g = 32 m/s2 , is: (1) 112 (2) 88 (3) 128 (4) 100

Q4. Distance of the centre of mass of a solid uniform cone from its vertex is z0 . If the radius of its base is R and its height is h then z0 is equal to: JEE Main 2015 (04 Apr) JEE Main Previous Year Paper (1) 3h2 (2) h2 8R 4R (3) 3h (4) 5h 4 8

Q5. Consider a thin uniform square sheet made of a rigid material. If its side is a, mass m and moment of inertia I about one of its diagonals, then: ma2 I < (1) I = ma224 (2) ma224 < 12 ma2 I = (3) I > ma212 (4) 12

Q5. A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length L(L ≫r) and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic): (1) mv2 (2) mv2 L−nr L−2nr (3) mv2 (4) Zero 2(L−nr)

Q5. A particle of mass m moving in the x direction with speed 2v is hit by another particle of mass 2m moving in the y direction with speed v. If the collision is perfectly inelastic, the percentage loss in the energy during the collision is close to: (1) 62% (2) 44% (3) 50% (4) 56%

Q6. From a solid sphere of mass M and radius R, a cube of the maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is: (1) 4MR2 (2) MR2 3√3π 32√2π (3) MR2 (4) 4MR2 16√2π 9√3π

Q6. A uniform solid cylindrical roller of mass m is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is a and it is rolling without slipping then the value of F is: (1) 3 ma (2) 2 ma 2 (3) 5 ma (4) ma 3 JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q6. A particle is moving in a circle of radius r under the action of a force F = αr2 which is directed towards centre of the circle. Total mechanical energy (kinetic energy + potential energy) of the particle is (take potential energy = 0 for r = 0): JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper (1) 5 6 αr3 (2) αr3 (3) 2 1 αr3 (4) 43 αr3

Q7. From a solid sphere of mass M and radius R, a spherical portion of radius ( R2 ) is removed as shown in the figure. Taking gravitational potential V = 0 at r = ∞, the potential at the centre of the cavity thus formed is ( G =gravitational constant) (1) −2GM (2) −GM R 2R (3) −GM (4) −2GM R 3R

Q7. A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R << L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of the star is T and its distance from the galaxy's axis is r, then (1) T ∝ √r (2) T ∝r (3) T ∝r2 (4) T 2 ∝r3

Q7. A uniform thin rod AB of length L has linear mass density μ(x) = a + bxL , where x is measured from A. If the CM of the rod lies at a distance of ( 127 L) from A, then a and b are related as: (1) 2a = b (2) a = 2b (3) a = b (4) 3a = 2b

Q8. A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0. 6 m. The height of the table from the ground is 0. 8 m. If the angular speed of the particle is 12 rad s−1 , the magnitude of its angular momentum about a point on the ground right under the center of the circle is: (1) 14 .4 kg m2 s−1 (2) 11.52 kg m2 s−1 (3) 20.16 kg m2 s−1 (4) 8.64 kg m2 s−1

Q8. If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by: (1) RT (2) 4RT (3) 4TR (4) 2TR

Q8. A pendulum made of a uniform wire of cross sectional area A has time period T. When an additional mass M is added to its bob, the time period changes to TM . If the Young's modulus of the material of the wire is Y , then 1 is equal to: Y ( g =gravitational acceleration) (1) T 2 A (2) T M 2 A −( TM ) Mg T ) Mg [1 ] [( −1] (3) T M 2 Mg (4) TM 2 A T ) A −( T ) Mg [( −1] [1 ]

Q9. If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter 2 cm then the Reynolds number for √π the flow is (density of water = 103 kg/m3 and viscosity of water = 10−3 Pa. s ) close to: (1) 5500 (2) 550 (3) 1100 (4) 11,000

Q9. Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average time of collision between molecules increases as V q , where V is the volume of the gas. The value of q is: (γ = CPCv ) (1) γ−1 (2) 3γ+5 2 6 (3) 3γ−5 (4) γ+1 6 2 JEE Main 2015 (04 Apr) JEE Main Previous Year Paper

Q10.Consider a spherical shell of radius R at temperature T. The black body radiation inside it can be considered as an ideal gas of photons with internal energy per unit volume u = UV ∝T 4 and pressure p = 13 ( UV ) . If the shell now undergoes an adiabatic expansion the relation between T and R is: (1) T ∝ 1 (2) T ∝e−R R3 (3) T ∝e−3R (4) T ∝ R1

Q10.An experiment takes 10 min to raise the temperature of water in a container from 0oC to 100oC and another 55 min to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of the water to be 1 cal (g∘C)−1 , the heat of vaporization according to this experiment will come out to be: (1) 530 cal g−1 (2) 550 cal g−1 (3) 540 cal g−1 (4) 560 cal g−1

Q11.In an ideal gas at temperature T, the average force that a molecule applies on the walls of a closed container depends on T as T q . A good estimate for q is: (1) 2 (2) 12 (3) 1 (4) 14

Q11.A solid body of constant heat capacity 1 J (℃)−1 is being heated by keeping it in contact with reservoirs in two ways: (i) Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies the same amount of heat. (ii) Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies the same amount of heat. In both, cases the body is brought from initial temperature 100 K to final temperature 200 K . Entropy change of the body in the two cases respectively is: Note: This question was awarded as a bonus since temperatures were given in centigrade instead of in Kelvin. Proper corrections are made in the question to avoid it. (1) 2 ln 2, 8 ln 2 (2) ln 2, 4 ln 2 (3) ln 2, ln 2 (4) ln 2, 2 ln 2