Practice Questions

Q3. A particle moves such that its position vector →r(t) = cos ωtˆi + sin ωtˆj where ω is a constant and t is time. Then which of the following statements is true for the velocity →v(t) and acceleration →a(t) of the particle: (1) →vis perpendicular to →rand →a is directed away (2) →vand →a both are perpendicular to →r from the origin (3) →vand →a both are parallel to →r (4) →vis perpendicular to →rand →a is directed towards the origin

Q3. The coordinates of the centre of mass of a uniform flag-shaped lamina (thin flat plate) of mass 4 kg. (The coordinates of the same are shown in the figure) are: (1) (1.25 m, 1.50 m) (2) (0.75 m, 1.75 m) (3) (0.75 m, 0.75 m) (4) (1 m, 1.75 m)

Q3. A particle starts from the origin at t = 0 with an initial velocity of 3.0ˆim/s and moves in the x −y plane with a constant acceleration + The x− coordinate of the particle at the instant when its y− (6.0ˆi 4.0ˆj)m/s2. coordinate is 32m is D meters. The value of D is: (1) 32 (2) 50 (3) 60 (4) 40

Q3. If the potential energy between two molecules is given by U = A + B , then at equilibrium, separation r6 r12 between molecules, and the potential energy are: (1) ( 2AB ) 1/6, −A22B (2) ( AB ) 1/6, 0 1 A2 , B ) 6 (3) ( 2BA ) 1/6, 4BA2 (4) ( 2A 2B

Q3. Two particles of equal mass m have respective initial velocities uˆi and u( ˆi+ˆj2 ) . They collide completely inelastically. The energy lost in the process is: (1) 1 mu2 (2) 1 mu2 3 8 (3) 3 mu2 (4) 4 √23 mu2

Q4. The acceleration due to gravity on the earth's surface at the poles is g and angular velocity of the earth about the axis passing through the pole is ω. An object is weighed at the equator and at a height h above the poles by using a spring balance. If the weights are found to be same, then h is: ( h ≪R, where R is the radius of the earth) (1) R2ω2 (2) R2ω2 2g g (3) R2ω2 (4) R2ω2 4g 8g

Q4. Mass per unit area of a circular disc of radius a depends on the distance r from its centre as σ(r) = A + Br . The moment of inertia of the disc about the axis, perpendicular to the plane and passing through its centre is: (1) 2πa4( A4 + aB5 ) (2) 2πa4( aA4 + B5 ) (3) πa4( A4 + aB5 ) (4) 2πa4( A4 + B5 )

Q4. Blocks of masses m, 2m, 4m and 8m are arranged in a line of a frictionless floor. Another block of mass m , moving with speed υ along the same line (see figure) collides with mass m in perfectly inelastic manner. All the subsequent collisions are also perfectly inelastic. By the time the last block of mass 8m starts moving the total energy loss is p% of the original energy. Value of ‘ p ’ is close to: (1) 77 (2) 94 (3) 37 (4) 87

Q4. The radius of gyration of a uniform rod of length l, about an axis passing through a point 4l away from the centre of the rod, and perpendicular to it, is: (1) 14 l (2) 18 l (3) (4) l l √748 √38

Q4. The linear mass density of a thin rod AB of length L varies from A to B as λ(x) = λ0(1 + Lx ), where x is the distance from A . If M is the mass of the rod then its moment of inertia about an axis passing through A and perpendicular to the rod : (1) 12 5 ML2 (2) 187 ML2 (3) 2 5 ML2 (4) 37 ML2

Q4. A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N . The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box? (1) 3280 J (2) 2780 J (3) 5690 J (4) 5250 J

Q4. Shown in the figure is a hollow ice-cream cone (it is open at top). If its mass is M, radius of its top is R and height, H , then its moment of inertia about its axis is (1) MR2 (2) M(R2+H2) 2 4 (3) MH2 (4) MR2 3 3

Q4. A uniform cylinder of mass M and radius R is to be pulled over a step of height a (a < R) by applying a force F at its centre ′O′ perpendicular to the plane through the axes of the cylinder on the edge of the step (see figure). The minimum value of F required is : (1) R−a 2 (2) R 2 Mg √( R−a ) −1 Mg √1 −( R ) (3) Mg Ra (4) Mg √1 −a2R2

Q4. A block of mass 1. 9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0. 1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m s−1 in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m s−2 . Assume there is no rotational motion and loss of energy after the collision is negligible.] (1) 21 J (2) 20 J (3) 19 J (4) 23 J

Q4. Pressure inside two soap bubbles are 1. 01 and 1. 02 atmosphere, respectively. The ratio of their volumes is : (1) 4 : 1 (2) 0. 8 : 1 (3) 8 : 1 (4) 2 : 1

Q4. Consider a uniform rod of mass M = 4m and length l pivoted about its centre. A mass m moving with velocity v making angle θ = π4 to the rod’s long axis collides with one end of the rod and sticks to it. The angular speed of the rod-mass system just after the collision is: (1) 3 v (2) 3 v 7√2 l 7 l (3) 3√2 v (4) 4 v 7 l 7 l

Q4. A wheel is rotating freely with an angular speed ω on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3I initially at rest is suddenly coupled to the same shaft. The resultant fractional loss in the kinetic energy of the system is: (1) 65 (2) 14 (3) 0 (4) 34

Q4. A capillary tube made of glass of radius 0. 15 mm is dipped vertically in a beaker filled with methylene iodide (surface tension = 0. 05 N m−1 , density = 667 kg m−3 ) which rises to height h in the tube. It is observed that the two tangents drawn from observed that the two tangents drawn from liquid-glass interfaces (from opp. sides of the capillary) make an angle of 60º with one another. Then h is close to ( g = 10 m s−2 ) (1) 0. 049 m (2) 0. 087 m (3) 0. 137 m (4) 0. 172 m

Q5. Consider two solid spheres of radii R1 = 1 m, R2 = 2 m and masses M1 and M2, respectively. The gravitational field due to sphere (1) and (2) are shown. The value of M1 is: M2 JEE Main 2020 (08 Jan Shift 1) JEE Main Previous Year Paper (1) 2 (2) 1 3 6 (3) 1 (4) 1 2 3

Q5. In an experiment to verify Stokes law, a small spherical ball of radius r and density ρ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water surface, then the value of h is proportional to: (ignore viscosity of air) (1) r4 (2) r (3) r3 (4) r2

Q5. On the x-axis and at a distance x from the origin, the gravitational field due to a mass distribution is given by Ax in the x-direction. The magnitude of the gravitational potential on the x-axis at a distance x, taking its (x2+a2)3/2 value to be zero at infinity is: (1) A (2) A (x2+a2)1/2 (x2+a2)3/2 (3) A(x2 + a2)1/2 (4) A(x2 + a2)3/2

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. Consider two uniform discs of the same thickness and different radii R1 = R and R2 = αR made of the same material. If the ratio of their moments of inertia I1 and I2 , respectively, about their axes is I1 : I2 = 1 : 16 then the value of α is : (1) 2√2 (2) √2 (3) 2 (4) 4

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

Q5. Four point masses, each of mass m , are fixed at the corners of a square of side I. The square is rotating with angular frequency ω, about an axis passing through one of the corners of the square and parallel to tis diagonal, as shown in the figure. The angular momentum of the square about the axis is (1) mℓ2ω (2) 4mℓ2ω (3) 3mℓ2ω (4) 2mℓ2ω JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper