Practice Questions

Q3. A particle of mass M originally at rest is subjected to a force whose direction is constant but magnitude varies T are constants. The force acts only for −( t−TT )2] where F0 and with time according to the relation F = F0[1 the time interval 2 T . The velocity v of the particle after time 2 T is: (1) 2 F 0 T (2) F0 T M 2M (3) 4 F 0 T (4) F0 T 3M 3M

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. 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. A circular hole of radius ( a2 ) is cut out of a circular disc of radius a as shown in figure. The centroid of the remaining circular portion with respect to point O will be: (1) 2 a (2) 5 a 3 6 (3) 1 a (4) 10 a 6 11

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. A body at rest is moved along a horizontal straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to: (1) t 32 (2) t 21 (3) t 14 (4) t 43

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. Statement I: A cyclist is moving on an unbanked road with a speed of 7 km h−1 and takes a sharp circular turn along a path of the radius of 2 m without reducing the speed. The static friction coefficient is 0. 2 . The cyclist will not slip and pass the curve (g = 9. 8 m s−2) Statement II : If the road is banked at an angle of 45° , cyclist can cross the curve of 2 m radius with the speed of 18. 5 km h−1 without slipping. In the light of the above statements, choose the correct answer from the options given below. (1) Statement I is incorrect and statement II is correct (2) Statement I is correct and statement II is incorrect (3) Both statement I and statement II are false (4) Both statement I and statement II are true

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. 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 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 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. 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. 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. 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. 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. 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 body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator? [Use g = GM = 9. 8 m s−2 and radius of earth, R = 6400 km.] R2 (1) 49. 17 N (2) 48. 83 N (3) 49. 83 N (4) 49 N

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 : 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. 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 steel block of 10 kg rests on a horizontal floor as shown. When three iron cylinders are placed on it as shown, the block and cylinders go down with an acceleration 0. 2 m s−2. The normal reaction R′ by the floor if mass of the iron cylinders are equal and of 20 kg each is (in N), [Take g = 10 m s−2 and μs = 0. 2] (1) 716 (2) 686 (3) 714 (4) 684

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: 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.

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