Practice Questions

Q5. The boxes of masses 2 kg and 8 kg are connected by a massless string passing over smooth pulleys. Calculate the time taken by box of mass 8 kg to strike the ground starting from rest. (g = 10 m s−2) (1) 0. 25 s (2) 0. 34 s (3) 0. 2 s (4) 0. 4 s JEE Main 2021 (27 Aug Shift 2) JEE Main Previous Year Paper

Q5. If the kinetic energy of a moving body becomes four times its initial kinetic energy, then the percentage change in its momentum will be: (1) 100% (2) 200% (3) 300% (4) 400%

Q5. The time period of a satellite in a circular orbit of the radius R is T. The period of another satellite in a circular orbit of the radius 9R is: (1) 9T (2) 27T (3) 12T (4) 3T

Q5. Given below are two statements: Statement I: In a diatomic molecule, the rotational energy at a given temperature obeys Maxwell's distribution. Statement II : In a diatomic molecule, the rotational energy at a given temperature equals the translational kinetic energy for each molecule. In the light of the above statements, choose the correct answer from the options given below: (1) Statement I is false but Statement II is true. (2) Statement I is true but Statement II is false. (3) Both Statement I and Statement II are true. (4) Both Statement I and Statement II are false. JEE Main 2021 (25 Feb Shift 2) JEE Main Previous Year Paper

Q5. Consider a situation in which a ring, a solid cylinder and a solid sphere roll down on the same inclined plane without slipping. Assume that they start rolling from rest and having identical diameter. The correct statement for this situation is (1) The sphere has the greatest and the ring has the (2) The ring has the greatest and the cylinder has the least velocity of the centre of mass at the bottom least velocity of the centre of mass at the bottom of the inclined plane. of the inclined plane. (3) All of them will have same velocity. (4) The cylinder has the greatest and the sphere has the least velocity of the centre of mass at the bottom of the inclined plane.

Q5. Angular momentum of a single particle moving with constant speed along circular path : (1) remains same in magnitude but changes in the (2) remains same in magnitude and direction direction (3) is zero (4) changes in magnitude but remains same in the direction

Q5. Four equal masses, m each are placed at the corners of a square of length (l) as shown in the figure. The moment of inertia of the system about an axis passing through A and parallel to DB would be : JEE Main 2021 (16 Mar Shift 1) JEE Main Previous Year Paper (1) ml2 (2) 2 ml2 (3) 3 ml2 (4) √3 ml2

Q5. An inclined plane making an angle of 30° with the horizontal is placed in a uniform horizontal electric field 200 NC as shown in the figure. A body of mass 1 kg and charge 5 mC is allowed to slide down from rest at a height of 1 m. If the coefficient of friction is 0. 2, find the time taken by the body to reach the bottom. [g = 9. 8 m s−2; sin 30°= 12 ; cos 30°= √32 ] (1) 0. 92 s (2) 1. 3 s (3) 0. 46 s (4) 2. 3 s

Q5. The figure shows two solid discs with radius R and r respectively. If mass per unit area is the same for both, what is the ratio of MI of bigger disc around axis AB (Which is ⊥ to the plane of the disc and passing through its centre) of MI of smaller disc around one of its diameters lying on its plane? Given M is the mass of the larger disc. ( MI stands for a moment of inertia) (1) R2 : r2 (2) 2r4 : R4 (3) 2R2 : r2 (4) 2R4 : r4

Q5. The minimum and maximum distances of a planet revolving around the Sun are 𝑥1 and 𝑥2. If the minimum speed of the planet on its trajectory is 𝑣0, then its maximum speed will be: (1) 𝑣0𝑥12 (2) 𝑣0𝑥22 𝑥22 𝑥12 𝑣0𝑥1 𝑣0𝑥2 (3) (4) 𝑥2 𝑥1

Q5. A person whose mass is 100 kg travels from Earth to Mars in a spaceship. Neglect all other objects in sky and take acceleration due to gravity on the surface of the Earth and Mars as 10 m s−2 and 4 m s−2 , respectively. Identify from the below figures, the curve that fits best for the weight of the passenger as a function of time. JEE Main 2021 (20 Jul Shift 1) JEE Main Previous Year Paper (1) (c) (2) (a) (3) (d) (4) (b)

Q5. A body of mass 𝑚 dropped from a height ℎ reaches the ground with a speed of 0 . 8√𝑔ℎ. The value of work done by the air-friction is: (1) -0 . 68𝑚𝑔ℎ (2) 𝑚𝑔ℎ (3) 0 . 64𝑚𝑔ℎ (4) 1 . 64𝑚𝑔ℎ

Q5. A bomb is dropped by a fighter plane flying horizontally. To an observer sitting in the plane, the trajectory of the bomb is a : (1) straight line vertically down the plane (2) parabola in a direction opposite to the motion of plane (3) parabola in the direction of motion of plane (4) hyperbola

Q5. Moment of inertia of a square plate of side l about the axis passing through one of the corner and perpendicular to the plane of square plate is given by: (1) Ml26 (2) 23 Ml2 (3) Ml2 (4) Ml212

Q5. Four identical solid spheres each of mass m and radius a are placed with their centres on the four corners of a square of side b. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is : (1) 85 ma2 + mb2 (2) 54 ma2 + 2mb2 (3) 85 ma2 + 2mb2 (4) 54 ma2

Q5. The instantaneous velocity of a particle moving in a straight line is given as v = αt + βt2 , where α and β are constants. The distance travelled by the particle between 1 s and 2 s is: (1) 3α + 7β (2) 32 α + 73 β (3) α 2 + β3 (4) 32 α + 72 β Q6. → A force F = + N acts on a body of mass 5 kg. If the body starts from rest, its position vector →rat (40ˆi 10ˆj) time t = 10 s will be + + m (1) (100ˆi 400ˆj) m (2) (100ˆi 100ˆj) + + m (3) (400ˆi 100ˆj) m (4) (400ˆi 400ˆj)

Q5. If one mole of an ideal gas at (P1, V1) is allowed to expand reversibly and isothermally ( A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B →C). Then it is restored to its initial state by a reversible adiabatic compression ( C to A ). The net workdone by the gas is equal to: (1) 0 (2) RT ln(2) − 2(γ−1) (3) − 2(γ−1)RT (4) RT [ln(2) 1 ] JEE Main 2021 (24 Feb Shift 2) JEE Main Previous Year Paper

Q5. Consider a uniform wire of mass M and length L. It is bent into a semicircle. Its moment of inertia about a line perpendicular to the plane of the wire passing through the centre is : (1) 1 ML2 (2) 2 ML2 4 π2 5 π2 (3) ML2 (4) 1 ML2 π2 2 π2

Q5. A system consists of two identical spheres each of mass 1 . 5 kg and radius 50 cm at the ends of a light rod. The distance between the centres of the two spheres is 5 m . What will be the moment of inertia of the system about an axis perpendicular to the rod passing through its midpoint? (1) 1 . 905 × 105 kg m2 (2) 18 . 75 kg m2 (3) 19 . 05 kg m2 (4) 1 . 875 × 105 kg m2

Q5. Four identical particles of equal masses 1 kg made to move along the circumference of a circle of radius 1 m under the action of their own mutual gravitational attraction. The speed of each particle will be: JEE Main 2021 (24 Feb Shift 1) JEE Main Previous Year Paper + 2√2 (1) √𝐺1 + 2√2 (2) √ 𝐺21 𝐺 2√2𝐺 (3) (4) √1 + √ 22√2 - 1 2

Q5. A geostationary satellite is orbiting around an arbitrary planet P at a height of 11R above the surface of P , R being the radius of P . The time period of another satellite in hours at a height of 2R from the surface of P is ________ has the time period of 24 hours. (1) 6√2 (2) 6 √2 (3) 3 (4) 5

Q6. Two identical particles of mass 1 kg each go round a circle of radius R , under the action of their mutual gravitational attraction. The angular speed of each particle is: (1) √ 2R3G (2) 21 √GR3 (3) 1 (4) 2R √1G √2GR3

Q6. When two soap bubbles of radii a and b(b > a) coalesce, the radius of curvature of common surface is: (1) ab (2) a+b b−a ab (3) b−a (4) ab ab a+b

Q6. Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R . Assertion A : The escape velocities of planet A and B are same. But A and B are of unequal mass. Reason R: The product of their mass and radius must be same. M1R1 = M2R2 In the light of the above statements, choose the most appropriate answer from the options given below : (1) Both A and R are correct and R is the correct (2) Both A and R are correct but R is NOT the explanation of A correct explanation of A (3) A is not correct but R is correct (4) A is correct but R is not correct

Q6. An electric appliance supplies 6000 J min−1 , heat to the system. If the system delivers a power of 90 W. How long it would take to increase the internal energy by 2. 5 × 103 J? (1) 2. 5 × 101 s (2) 2. 5 × 102 s (3) 2. 4 × 103 s (4) 4. 1 × 101 s