Practice Questions

Q3. Water drops are falling from a nozzle of a shower onto the floor from a height of 9. 8 m. The drops fall at a regular interval of time. When the first drop strikes the floor, at that instant, the third drop begins to fall. Locate the position of second drop from the floor when the first drop strikes the floor. (1) 2. 94 m (2) 4. 18 m (3) 2. 45 m (4) 7. 35 m

Q3. A block of mass m slides along a floor while a force of magnitude F is applied to it at an angle θ as shown in figure. The coefficient of kinetic friction is μK . Then, the block's acceleration a is given by : ( g is acceleration due to gravity) (1) −Fm cos θ −μK(g −Fm sin θ) (2) mF cos θ −μK(g −Fm sin θ) (3) m F cos θ −μK(g + mF sin θ) (4) mF cos θ + μK(g −Fm sin θ)

Q3. A particle is moving with uniform speed along the circumference of a circle of radius R under the action of a central fictitious force F which is inversely proportional to R3 . Its time period of revolution will be given by : (1) T ∝R 43 (2) T ∝R 25 (3) T ∝R 32 (4) T ∝R2

Q3. A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time t is proportional to :- (1) t 32 (2) t 23 (3) t (4) t 21

Q3. If velocity 𝑉 time 𝑇 and force 𝐹 are chosen as the base quantities, the dimensions of the mass will be : (1) 𝐹𝑉𝑇-1 (2) 𝐹𝑇-1𝑉-1 (3) 𝐹𝑇2 𝑉 (4) 𝐹𝑇𝑉-1

Q3. Three objects A, B and C are kept in a straight line on a frictionless horizontal surface. The masses of A, B and C are m, 2m and 2m respectively. A moves towards B with a speed of 9 m s−1 and makes an elastic collision with it. Thereafter B makes a completely inelastic collision with C. All motions occur along the same straight line. The final speed of C is : (1) 6 m s−1 (2) 9 m s−1 (3) 4 m s−1 (4) 3 m s−1

Q3. Moment of inertia M . I . of four bodies, having same mass and radius, are reported as; 𝐼1 = M . I . of thin circular ring about its diameter, 𝐼2 = M . I . of circular disc about an axis perpendicular to disc and going through the centre, 𝐼3 = M . I . of solid cylinder about its axis and 𝐼4 = M . I . of solid sphere about its diameter. Then: 5 (1) 𝐼1 + 𝐼2 = 𝐼3 + 2𝐼4. (2) 𝐼1 + 𝐼3 < 𝐼2 + 𝐼4 (3) 𝐼1 = 𝐼2 = 𝐼3 > 𝐼4 (4) 𝐼1 = 𝐼2 = 𝐼3 < 𝐼4

Q3. The ranges and heights for two projectiles projected with the same initial velocity at angles 42° and 48° with the horizontal are 𝑅1, 𝑅2 and 𝐻1, 𝐻2 respectively. Choose the correct option: (1) 𝑅1 = 𝑅2 and 𝐻1 = 𝐻2 (2) 𝑅1 = 𝑅2 and 𝐻1 < 𝐻2 (3) 𝑅1 > 𝑅2 and 𝐻1 = 𝐻2 (4) 𝑅1 < 𝑅2 and 𝐻1 < 𝐻2 JEE Main 2021 (01 Sep Shift 2) JEE Main Previous Year Paper

Q3. Which of the following is not a dimensionless quantity? (1) Power factor (2) Quality factor (3) Permeability of free space (μ0) (4) Relative magnetic permeability (μr)

Q3. A scooter accelerates from rest for time t1 at constant rate a1 and then retards at constant rate a2 for time t2 and comes to rest. The correct value of t1 will be : t2 (1) a2 (2) a1 a1 a2 (3) a1+a2 (4) a1+a2 a1 a2

Q3. The initial mass of a rocket is 1000 kg. Calculate at what rate the fuel should be burnt so that the rocket is given an acceleration of, 20 m s−2 . The gases come out at a relative speed of 500 m s−1 , with respect to the rocket: [Use g = 10 m s−2] (1) 10 kg s−1 (2) 60 kg s−1 (3) 500 kg s−1 (4) 6. 0 × 102 kg s−1

Q3. Match List - I with List - II : List - I List - II a Magnetic induction i ML2 T−2 A−1 b Magnetic flux ii M0 L−1 A c Magnetic permeability iii MT−2 A−1 d Magnetization iv MLT−2 A−2 Choose the most appropriate answer from the options given below : (1) (a) −(iii), (b) −(ii), (c) −(iv), (d) −(i) (2) (a) −(iii), (b) −(i), (c) −(iv), (d) −(ii) (3) (a) −(ii), (b) −(iv), (c) −(i), (d) −(iii) (4) (a) −(ii), (b) −(i), (c) −(iv), (d) −(iii)

Q3. A boy is rolling a 0. 5 kg ball on the frictionless floor with the speed of 20 m s−1. The ball gets deflected by an obstacle on the way. After deflection it moves with 5% of its initial kinetic energy. What is the speed of the ball now? (1) 19. 0 m s−1 (2) 4. 4 m s−1 (3) 14. 41 m s−1 (4) 1. 00 m s−1 →

Q3. A helicopter is flying horizontally with a speed v at an altitude h has to drop a food packet for a man on the ground. What is the distance of helicopter from the man when the food packet is dropped ? (1) √2ghv2+1h2 (2) √2ghv2 + h2 + h2 + h2 √2v2g (3) √2ghv2 (4) h

Q3. A rubber ball is released from a height of 5 m above the floor. It bounces back repeatedly, always rising to 10081 of the height through which it falls. Find the average speed of the ball. (Take g = 10 m s−2 ) (1) 3. 0 m s−1 (2) 3. 5 m s−1 (3) 2. 0 m s−1 (4) 2. 50 m s−1

Q3. The relation between time t and distance x for a moving body is given as t = mx2 + nx, where m and n are constants. The retardation of the motion is: (When v stands for velocity) (1) 2mv3 (2) 2mnv3 (3) 2nv3 (4) 2n2v3

Q3. Two billiard balls of equal mass 30 g strike a rigid wall with same speed of 108 kmph (as shown) but at different angles. If the balls get reflected with the same speed, then the ratio of the magnitude of impulses imparted to ball 𝑎 and ball 𝑏 by the wall along 𝑋 direction is: JEE Main 2021 (25 Jul Shift 1) JEE Main Previous Year Paper (1) 1: 1 (2) √2: 1 (3) 2: 1 (4) 1: √2

Q3. An engine of a train, moving with uniform acceleration, passes the signal-post with velocity u and the last compartment with velocity v. The velocity with which middle point of the train passes the signal post is : (1) u+v (2) 2 √v2+u22 (3) v−u (4) 2 √v2−u22

Q3. The motion of a mass on a spring, with spring constant K is as shown in figure. The equation of motion is given by, x(t) = A sin ωt+B cos ωt with ω = . √Km Suppose that at time t = 0, the position of mass is x(0) and velocity v(0), then its displacement can also be represented as x(t) = C cos(ωt −ϕ), where C and ϕ are (1) v(0) (2) x(0)ω + ϕ = C = √2v(0)2ω2 ω2 x(0)2, tan−1( 2v(0) ) + x(0)2, ϕ = tan−1( x(0)ω ) C = √2v(0)2 (3) x(0)ω (4) v(0) C = + ϕ = C = + ϕ = ω2 x(0)2, tan−1( x(0)ω ) ω2 x(0)2, tan−1( v(0) ) √v(0)2 √v(0)2

Q4. A boy reaches the airport and finds that the escalator is not working. He walks up the stationary escalator in time t1. If he remains stationary on a moving escalator then the escalator takes him up in time t2. The time taken by him to walk up on the moving escalator will be: (1) t1t2 (2) t1+t2 t2−t1 2 (3) t1t2 (4) t2 −t1 t2+t1

Q4. A player kicks a football with an initial speed of 25 m s−1 at an angle of 45° from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion? (Take g = 10 m s−2 ) (1) hmax = 15. 625 m, T = 1. 77 s (2) hmax = 3. 54 m, T = 0. 125 s (3) hmax = 10 m, T = 2. 5 s (4) hmax = 15. 625 m, T = 3. 54 s

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. 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. Thermodynamic process is shown below on a P −V diagram for one mole of an ideal gas. If V2 = 2V1 , then the ratio of temperature T2 is : T1 (1) √2 (2) 1 √2 (3) 1 (4) 2 2

Q4. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Moment of inertia of a circular disc of mass 𝑀 and radius 𝑅 about 𝑋, 𝑌 axes (passing through its plane) and Z-axis which is perpendicular to its plane were found to be 𝐼x, 𝐼y and 𝐼z, respectively. The respective radii of gyration about all the three axes will be the same. Reason R: A rigid body making rotational motion has fixed mass and shape. In the light of the above statements, choose the most appropriate answer from the options given below: (1) Both A and R are correct but R is not the correct (2) A is not correct but R is correct. explanation of A. (3) A is correct but R is not correct. (4) Both A and R are correct and R is the correct explanation of A.