Practice Questions

Q1. Let L, R, C and V represent inductance, resistance, capacitance and voltage, respectively. The dimension of L in SI units will be: RCV (1) [LTA] (2) [A−1] (3) [LT 2] (4) [LA−2]

Q2. A ball is thrown upward with an initial velocity V0 from the surface of the earth. The motion of the ball is affected by a drag force equal to mγv2 (where m is mass of the ball, v is its instantaneous velocity and γ is a constant). Time taken by the ball to rise to its zenith is: (1) 1 (2) 1 g √γg ln(1 + √γg V0) √γg tan−1(√γ V0) (3) 1 (4) 1 g g √γg sin−1(√γ V0) √2γg tan−1(√2γ V0)

Q3. In a car race on straight road, car A takes a time t less than car B at the finish and passes finishing point with a speed v more than that of car B. Both the cars start from rest and travel with constant acceleration a1 and a2 respectively. Then v is equal to: (1) 2a1a2 t (2) a1+a2 t a1+a2 2 (3) √a1a2t (4) √2a1a2t

Q3. A simple pendulum, made of a string of length l and a bob of mass m, is released from a small angle θ0. It strikes a block of mass M, kept on horizontal surface at its lowest point of oscillations, elastically. It bounces back and goes up to an angle θ1. Then M is given by: (1) m( θ0−θ1θ0+θ1 ) (2) m( θ0−θ1θ0+θ1 ) (3) m θ0+θ1 (4) m θ0−θ1 2 ( θ0−θ1 ) 2 ( θ0+θ1 )

Q3. A body is projected at t = 0 with a velocity 10 ms−1 at an angle of 60∘ with the horizontal. The radius of curvature of its trajectory at t = 1 s is R. Neglecting air resistance and taking acceleration due to gravity g = 10 ms−2 , the value of R is: (1) 10.3 m (2) 2.8 m (3) 2.5 m (4) 5.1 m

Q4. A body of mass 1 kg falls freely from a height of 100 m, on a platform of mass 3 kg which is mounted on a spring having spring constant k = 1.25 × 106 N/m. The bodysticks to the platform and the spring's maximum compression is found to be x. Given that g = 10 ms−2, the value of x will be close to : (1) 40 cm (2) 4 cm (3) 80 cm (4) 8 cm −−−Q5. → → → A slab is subjected to two forces F1 and F2 of same magnitude F as shown in the figure. Force F2 is in XY- plane while force F1 acts along z -axis at the point (2→i + 3→j). The moment of these forces about point O will be: (1) (3^i −2^j + 3^k) F (2) (3^i −2^j −3^k)F (3) (3^i + 2^j −3^k)F (4) (3^i + 2^j + 3^k)F

Q5. A solid sphere of mass M and radius R is divided into two unequal parts. The first part has a mass of and is 8 converted into uniform disc of radius 2R . The second part is converted into a uniform solid sphere. Let I1 be the moment of inertia of the disc about its axis and I2 be the moment of inertia of the new sphere about its axis. The ratio I1 / I2 is given by: (1) 140 (2) 185 (3) 65 (4) 285 JEE Main 2019 (10 Apr Shift 2) JEE Main Previous Year Paper

Q5. A person of mass 𝑀 is sitting on a swing of length 𝐿 and swinging with and an angular amplitude θ0 . If the person stands up when the swing passes through its lowest point, the work done by him, assuming that his centre of mass moves by a distance 𝑙 𝑙< < 𝐿, is close to: (1) 𝑀𝑔𝑙 (1 - θ02 ) (2) θ02 𝑀𝑔𝑙(1 + ) 2 (3) 𝑀𝑔𝑙 (4) 𝑀𝑔𝑙(1 + θ02 )

Q5. A particle of mass m is moving with speed 2v and collides with a mass 2m moving with speed v in the same direction. After the collision, the first mass is stopped completely while the second one splits into two particles each of mass m, which move at an angle 45o with respect to the original direction. The speed of each of the moving particle will be (1) √2v (2) v √2 (3) 2√2v (4) v (2√2)

Q5. A piece of wood of mass 0.03 kg is dropped from the top of a 100 m height building. At the same time, a bullet of mass 0.02 kg is fired vertically upward, with a velocity 100 ms−1, from the ground. The bullet gets JEE Main 2019 (10 Jan Shift 1) JEE Main Previous Year Paper embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is: (g = 10 ms−2) (1) 40 m (2) 20 m (3) 10 m (4) 30 m

Q5. Three blocks A, B and C are lying on a smooth horizontal surface, as shown in the figure. A and B have equal masses, 𝑚 while C has mass 𝑀. Block A is given an initial speed 𝑣 towards B due to which it collides with B perfectly inelastically. The combined mass collides with 𝐶, also perfectly inelastically . 5 of the initial kinetic 6th energy is lost in the whole process. What is the value of 𝑀/ 𝑚? (1) 3 (2) 4 (3) 5 (4) 2 𝑚

Q6. Two masses 𝑚 and are connected at the two ends of a massless rigid rod of length 𝑙. The rod is suspended by 2 a thin wire of torsional constant 𝑘 at the centre of mass of the rod-mass system (see figure). Because of torsional constant 𝑘, the restoring torque is 𝜏= 𝑘𝜃 for angular displacement 𝜃. If the rod is rotated by 𝜃0 and released, JEE Main 2019 (09 Jan Shift 1) JEE Main Previous Year Paper the tension in it when it passes through its mean position will be: (1) 𝑘𝜃02 (2) 3𝑘𝜃02 𝑙 (3) 2𝑘𝜃02 (4) 𝑘𝜃02 𝑙 𝑙

Q6. A satellite of mass M is in a circular orbit of radius R about the center of the earth. A meteorite of the same mass, falling towards the earth, collides with the satellite completely inelastic. The speeds of the satellite and the meteorite are the same, just before the collision. The subsequent motion of the combined body will be: (1) In an elliptical orbit (2) Such that it escapes to infinity (3) In a circular orbit of a different radius (4) In the same circular orbit of radius R

Q6. A thin circular plate of mass 𝑀 and radius 𝑅 has its density varying as ρ ( 𝑟) =ρ0r with 𝜌0 as constant and 𝑟 is the distance from its centre. The moment of Inertia of the circular plate about an axis perpendicular to the plate and passing through its edge is 𝐼= 𝑎𝑀𝑅2. The value of the coefficient 𝑎 is: (1) 3 (2) 1 (3) 8 (4) 3 5 2 5 2

Q7. A rectangular solid box of length 0.3 m is held horizontally, with one of its sides on the edge of a platform of height 5 m . When released, it slips off the table in a very short time τ = 0.01 s , remaining essentially horizontal. The angle by which it would rotate when it hits the ground will be (in radians) close to: (1) 0.5 (2) 0.3 (3) 0.02 (4) 0.28

Q7. A satellite is revolving in a circular orbit at a height h from the carth surface, such that h << R where R is the radius of the earth. Assuming that the effect of earth"s atmosphere can be neglected the minimum increase in the speed required so that the satellite could escape from the gravitational field of earth is (1) √2gR (2) √gR (3) √gR2 (4) √gR(√2 −1)

Q7. A circular disc of radius 𝑏 has a hole of radius a at its centre(see figure). If the mass per unit area of the disc 𝜎0 varies as then, the radius of gyration of the disc about its axis passing through the center is 𝑟 (1) 𝑎+ 𝑏 (2) + 𝑏2 + 𝑎𝑏 3 √𝑎2 3 + 𝑏2 + 𝑎𝑏 (3) 𝑎+ 𝑏 (4) √𝑎2 2 2

Q7. Four identical particles of mass M are located at the corners of a square of side ‘𝑎’ . What should be their speed if each of them revolves under the influence of other’s gravitational field in a circular orbit circumscribing the JEE Main 2019 (08 Apr Shift 1) JEE Main Previous Year Paper square? (1) GM (2) GM (3) GM (4) GM 1.35√ a 1.21√ a 1.41√ a 1.16√ a

Q7. A straight rod of length L extends from x = a to x = L + a. The gravitational force it exerts on a point mass 'm' at x = 0, if the mass per unit length of the rod is A + Bx2, is given by: JEE Main 2019 (12 Jan Shift 1) JEE Main Previous Year Paper (1) Gm[A( a+L1 −1a ) + BL] (2) Gm[A( a+L1 −1a ) −BL] (3) Gm[A( a1 − a+L1 ) −BL] (4) Gm[A( a1 − a+L1 ) + BL]

Q8. A satellite is moving with a constant speed v in circular orbit around the earth. An object of mass 'm' is ejected from the satellite such that it just escapes from the gravitational pull of the earth. At the time of ejection, the kinetic energy of the object is: (1) 23 m v2 (2) m v2 (3) 12 m v2 (4) 2 m v2

Q8. A test particle is moving in a circular orbit in the gravitational field produced by a mass density ρ(r) = K . r2 Identify the current relation between the radius R of the particle’s orbit and its period T : JEE Main 2019 (09 Apr Shift 2) JEE Main Previous Year Paper (1) TR is a constant (2) T 2/R3 is a constant (3) T/R is a constant (4) T/R2 is a constant

Q8. Two stars of masses 3 × 1031 kg each, and at distance 2 × 1011 m rotate in a plane about their common centre of mass O. A meteorite passes through O moving perpendicular to the stars,s rotation plane. In order to escape from the gravitational field of this double star, the minimum speed that meteorite should have at O is ( Take Gravitational constant G = 6.67 × 10−11 N m2 kg−2 ) (1) 2.4 × 104 m s−1 (2) 3.8 × 104 m s−1 (3) 2.8 × 105 m s−1 (4) 1.4 × 105 m s−1

Q9. Ice at −20∘C is added to 50 g of water at 40∘C, When the temperature of the mixture reaches 0∘C, it is found that 20 g of ice is still unmelted. The amount of ice added to the water was close to (Specific heat of water = 4.2 J/g/∘C Specific heat of Ice = 2.1 J/g/∘C Heat of fusion of water at 0∘C = 334 J/g) (1) 50 g (2) 100 g (3) 60 g (4) 40 g

Q10.A 25 × 10−3 m3 volume cylinder is filled with 1 mol of O2 gas at room temperature (300 K) . The molecular diameter of O2 , and its root mean square speed, are found to be 0.3 nm and 200 m/s , respectively. What is the average collision rate (per second) for an O2 molecule? (1) ~1011 (2) ~1012 (3) ~1010 (4) ~1013

Q11.A Carnot engine has an efficiency of 1 6 . When the temperature of the sink is reduced by 62 ℃ , its efficiency is doubled. The temperatures of the source and the sink are, respectively, JEE Main 2019 (12 Apr Shift 2) JEE Main Previous Year Paper (1) 124 ℃, 62 ℃ (2) 37 ℃, 99 ℃ (3) 99 ℃, 37 ℃ (4) 62 ℃, 124 ℃