Practice Questions

Q4. Given below is the plot of a potential energy function U(x) for a system, in which a particle is in one dimensional motion, while a conservative force F(x) acts on it. Suppose that Emech = 8 J, the incorrect statement for this system is : (1) at x > x4, K. E . is constant throughout the (2) at x < x1, K. E . is smallest and the particle is region. moving at the slowest speed. (3) at x = x2, K. E . is greatest and the particle is (4) at x = x3, K. E. = 4 J moving at the fastest speed.

Q4. A balloon was moving upwards with a uniform velocity of 10 m s−1 . An object of finite mass is dropped from the balloon when it was at a height of 75 m from the ground level. The height of the balloon from the ground when object strikes the ground was around: (takes the value of g as 10 m s−2 ) (1) 300 m (2) 200 m (3) 125 m (4) 250 m

Q4. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Body P having mass M moving with speed u has head-on collision elastically with another body Q having mass m initially at rest. If m ≪M , body Q will have a maximum speed equal to 2u after collision. Reason R : During elastic collision, the momentum and kinetic energy are both conserved. In the light of the above statements, choose the most appropriate answer from the options given below: (1) A is correct but R is not correct. (2) A is not correct but R is correct. (3) Both A and R are correct and R is the correct (4) Both A and R are correct but R is NOT the correct explanation of A explanation of A

Q4. The trajectory of a projectile in a vertical plane is y = αx −βx2, where α and β are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection θ and the maximum height attained H are respectively given by (1) tan−1 α, 4α2β (2) tan−1( αβ ), α2β (3) tan−1 β, α22β (4) tan−1 α, α24β

Q4. A sphere of mass 2 kg and radius 0. 5 m is rolling with an initial speed of 1 m s−1 goes up an inclined plane which makes an angle of 30° with the horizontal plane, without slipping. How low will the sphere take to return to the starting point A ? (1) 0. 60 s (2) 0. 52 s (3) 0. 56 s (4) 0. 80 s

Q4. A particle of mass m is suspended from a ceiling through a string of length L. The particle moves in a horizontal circle of radius r such that r = L . The speed of particle will be : √2 (1) √rg (2) √2rg (3) √rg2 (4) 2√rg

Q4. A thin circular ring of mass M and radius r is rotating about its axis with an angular speed ω. Two particles having mass m each are now attached at diametrically opposite points. The angular speed of the ring will become: (1) ω M (2) ω M+2M m M+m M m M−2 (3) ω (4) ω m m M+2 M+2

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. 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 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. 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. 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. 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. 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. 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. 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. 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. 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 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

Q5. Two satellites A and B of masses 200 kg and 400 kg are revolving round the earth at height of 600 km and 1600 km respectively. If TA and TB are the time periods of A and B respectively then the value of TB −TA : [ Given : radius of earth = 6400 km, mass of earth = 6 × 1024 kg ] (1) 4. 24 × 103 s (2) 3. 33 × 102 s (3) 1. 33 × 103 s (4) 4. 24 × 102 s

Q5. A mass M hangs on a massless rod of length l which rotates at a constant angular frequency. The mass M moves with steady speed in a circular path of constant radius. Assume that the system is in steady circular JEE Main 2021 (17 Mar Shift 1) JEE Main Previous Year Paper motion with constant angular velocity ω. The angular momentum of M about point A is LA which lies in the positive z direction and the angular momentum of M about B is LB. The correct statement for this system is: (1) LA and LB are both constant in magnitude and (2) LB is constant in direction with varying direction magnitude (3) LB is constant, both in magnitude and direction (4) LA is constant, both in magnitude and direction

Q5. Two narrow bores of diameter 5. 0 mm and 8. 0 mm are joined together to form a U−shaped tube open at both ends. If this U−tube contains water, what is the difference in the level of two limbs of the tube. [Take surface tension of water T = 7. 3 × 10−2 N m−1 , angle of contact = 0, g = 10 m s−2 and density of water = 1. 0 × 103 kg m−3] (1) 5. 34 mm (2) 3. 62 mm (3) 2. 19 mm (4) 4. 97 mm JEE Main 2021 (26 Aug Shift 1) JEE Main Previous Year Paper

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. What will be the nature of flow of water from a circular tap, when its flow rate increased from 0. 18 L (min)−1 to 0. 48 L (min)−1? The radius of the tap and viscosity of water are 0. 5 cm and 10−3 Pa s, respectively. (Density of water : 103 kg m−3 ) JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper (1) Unsteady to steady flow (2) Remains steady flow (3) Remains turbulent flow (4) Steady flow to unsteady flow