Tiêu đề 04. MOtion in a plane Hard.pdf ✅

1. A body of mass 2 kg has an initial velocity of 3 m/s along OE and it is subjected to a force of 4 Newton’s in OF direction perpendicular to OE. The distance of the body from O after 4 seconds will be (a) 12 m (b) 28 m (c) 20 m (d) 48 m 2. A body starts from the origin with an acceleration of 6 m/s2 along the x-axis and 8 m/s2 along the y-axis. Its distance from the origin after 4 seconds will be (a) 56 m (b) 64 m (c) 80 m (d) 128 m 3. A projectile is fired at 30o to the horizontal. The vertical component of its velocity is 80 ms–1 . Its time of flight is T. What will be the velocity of the projectile at t = T/2 (a) 80 ms–1 (b) 80 3 ms–1 (d) (80/ 3 ) ms–1 (d) 40 ms–1 4. A particle is projected from point O with velocity u in a direction making an angle  with the horizontal. At any instant its position is at point P at right angles to the initial direction of projection. Its velocity at point P is (a) u tan (b) u cot (c) u cosec (d) u sec 5. A particle P is projected with velocity u1 at an angle of 30o with the horizontal. Another particle Q is thrown vertically upwards with velocity u2 from a point vertically below the highest point of path of P. The necessary condition for the two particles to collide at the highest point is (a) u1 = u2 (b) 1 2 u = 2u (c) 2 2 1 u u = (d) 1 2 u = 4u 6. Two seconds after projection a projectile is travelling in a direction inclined at 30o to the horizontal after one more sec, it is travelling horizontally, the magnitude and direction of its velocity are (a) o 2 20 m/sec,60 (b) o 20 3 m/sec, 60 (c) o 6 40 m/sec, 30 (d) o 40 6 m/sec, 30 7. A body is projected up a smooth inclined plane (length = 20 2 m ) with velocity u from the point M as shown in the figure. The angle of inclination is 45o and the top is connected to a well of diameter 40 m. If the body just manages to cross the well, what is the value of v (a) 1 40 − ms (b) 1 40 2 − ms (c) 1 20 − ms (d) 1 20 2 − ms 8. A particle of mass 100 g is fired with a velocity 20 msec–1 making an angle of 30o with the horizontal. When it rises to the highest point of its path then the change in its momentum is (a) 1 3 sec − kgm (b) 1/2 kgmsec–1 (c) 1 2 sec − kgm (d) 1 kgmsec–1 9. Two equal masses (m) are projected at the same angle () from two points separated by their range with equal velocities (v). The momentum at the point of their collision is (a) Zero (b) 2 mvcos (c) – 2 mvcos (d) None 10. A particle of mass m is projected with velocity v making an angle of 45o with the horizontal. The magnitude of the angular momentum of the particle about the point of projection when the particle is at its maximum height is (where g = acceleration due to gravity) (a) Zero (b) mv3 / (4 2g) (c) mv3 / ( 2g) (d) mv2 /2g 11. Two particles are separated at a horizontal distance x as shown in figure. They are projected at the same time as shown in figure with different initial speed. The time after which the horizontal distance between the particles become zero is (a) u /2x (b) x/u (c) 2u/x (d) u/x 12. A particle is projected from a point O with a velocity u in a direction making an angle  upward with the horizontal. After some time at point P it is moving at right angle with its initial direction of projection. The time of flight from O to P is (a) g u sin (b) g u cosec (c) g u tan  (d) g u sec 13. A ball is projected upwards from the top of tower with a velocity 50 ms–1 making angle 30o with the horizontal. The height of the tower is 70 m. After how many seconds from the instant of throwing will the ball reach the ground (a) 2.33 sec (b) 5.33 sec (c) 6.33 sec (d) 9.33 sec 60o 30o u x u / 3 A B 40 m 45o M u2 u1 30o P Q
14. If for a given angle of projection, the horizontal range is doubled, the time of flight becomes (a) 4 times (b) 2 times (c) 2 times (d) 1 / 2 times 15. A particle is thrown with velocity u at an angle  from the horizontal. Another particle is thrown with the same velocity at an angle  from the vertical. The ratio of times of flight of two particles will be (a) Tan 2  : 1 (b) Cot 2  : 1 (c) Tan  : 1 (d) Cot  : 1 16. Figure shows four paths for a kicked football. Ignoring the effects of air on the flight, rank the paths according to initial horizontal velocity component, highest first (a) 1, 2, 3, 4 (b) 2, 3, 4, 1 (c) 3, 4, 1, 2 (d) 4, 3, 2, 1 17. A projectile thrown with a speed v at an angle  has a range R on the surface of earth. For same v and , its range on the surface of moon will be (a) R/6 (b) 6 R (c) R/36 (d) 36 R 18. A projectile is thrown into space so as to have maximum horizontal range R. Taking the point of projection as origin, the co-ordinates of the point where the speed of the particle is minimum are (a) (R, R) (b)       2 , R R (c)       4 , 2 R R (d)       4 , R R 19. The speed of a projectile at the highest point becomes 2 1 times its initial speed. The horizontal range of the projectile will be (a) g u 2 (b) g u 2 2 (c) g u 3 2 (d) g u 4 2 20. A large number of bullets are fired in all directions with same speed u. What is the maximum area on the ground on which these bullets will spread (a) g u 2  (b) 2 4 g u  (c) 2 4 2 g u  (d) 2 2 2 g u  21. A projectile is projected with initial velocity ) / . ˆ 8 ˆ (6i + j m sec If g = 10 ms–2 , then horizontal range is (a) 4.8 metre (b) 9.6 metre (c) 19.2 metre (d) 14.0 metre 22. A projectile thrown with an initial speed u and angle of projection 15o to the horizontal has a range R. If the same projectile is thrown at an angle of 45o to the horizontal with speed 2u, its range will be (a) 12 R (b) 3 R (c) 8 R (d) 4 R 23. The velocity at the maximum height of a projectile is half of its initial velocity of projection u. Its range on the horizontal plane is (a) 3u / 2g 2 (b) u / 3g 2 (c) 3u / 2g 2 (d) 3u / g 2 24. A projectile is thrown from a point in a horizontal place such that its horizontal and vertical velocity component are 9.8 m/s and 19.6 m/s respectively. Its horizontal range is (a) 4.9 m (b) 9.8 m (c) 19.6 m (d) 39.2 m 25. A particle is projected with a velocity v such that its range on the horizontal plane is twice the greatest height attained by it. The range of the projectile is (where g is acceleration due to gravity) (a) g v 5 4 2 (b) 2 5 4 v g (c) g v 2 (d) g v 5 4 2 26. The range R of projectile is same when its maximum heights are h1 and h2. What is the relation between R and h1 and h2 (a) R = h1h2 (b) R = 2h1h2 (c) R = 2 h1h2 (d) R = 4 h1h2 27. A grasshopper can jump maximum distance 1.6 m. It spends negligible time on the ground. How far can it go in 10 seconds (a) 5 2 m (b) 10 2 m (c) 20 2 m (d) 40 2 m 28. A projectile is thrown with an initial velocity of , ˆ ˆ v = ai + bj if the range of projectile is double the maximum height reached by it then (a) a = 2b (b) b = a (c) b = 2a (d) b = 4a 29. A ball thrown by one player reaches the other in 2 sec. the maximum height attained by the ball above the point of projection will be about (a) 10 m (b) 7.5 m (c) 5 m (d) 2.5 m 30. Two stones are projected with the same magnitude of velocity, but making different angles with horizontal. The angle of projection of one is /3 and its maximum height is Y, the maximum height attained by the other stone with as /6 angle of projection is (a) Y (b) 2 Y (c) 3 Y (d) 3 Y 0 1 2 3 4 y x
31. If the initial velocity of a projectile be doubled. Keeping the angle of projection same, the maximum height reached by it will (a) Remain the same (b) Be doubled (c) Be quadrupled (d) Be halved 32. Pankaj and Sudhir are playing with two different balls of masses m and 2m respectively. If Pankaj throws his ball vertically up and Sudhir at an angle , both of them stay in our view for the same period. The height attained by the two balls are in the ratio (a) 2 : 1 (b) 1 : 1 (c) 1 : cos (d) 1 : sec 33. A boy aims a gun at a bird from a point, at a horizontal distance of 100 m. If the gun can impart a velocity of 500 ms–1 to the bullet. At what height above the bird must he aim his gun in order to hit it (take g = 10 ms–2 ) (a) 20 cm (b) 10 cm (c) 50 cm (d) 100 cm 34. The maximum horizontal range of a projectile is 400 m. The maximum height attained by it will be (a) 100 m (b) 200 m (c) 400 m (d) 800 m 35. Two bodies are projected with the same velocity. If one is projected at an angle of 30o and the other at an angle of 60o to the horizontal, the ratio of the maximum heights reached is (a) 3 : 1 (b) 1 : 3 (c) 1 : 2 (d) 2 : 1 36. A man can throw a stone 80 m. The maximum height to which he can raise the stone is (a) 10 m (b) 15 m (c) 30 m (d) 40 m 37. A ball is thrown at different angles with the same speed u and from the same points and it has same range in both the cases. If y1 and y2 be the heights attained in the two cases, then y1 + y 2 = (a) g u 2 (b) g u 2 2 (c) g u 2 2 (d) g u 4 2 38. A projectile is projected with a kinetic energy K. Its range is R. It will have the minimum kinetic energy, after covering a horizontal distance equal to (a) 0.25 R (b) 0.5 R (c) 0.75 R (d) R 39. A particle is projected making angle 450 with horizontal having kinetic energy K. The kinetic energy at highest point will be (a) 2 K (b) 2 K (c) 2K (d) K 40. Two balls of same mass are projected one vertically upwards and the other at angle 600 with the vertical. The ratio of their potential energy at the highest point is (a) 3 : 2 (b) 2 : 1 (c) 4 : 1 (d) 4 : 3 41. A ball is thrown at an angle  with the horizontal. Its initial kinetic energy is 100 J and it becomes 30 J at the highest point. The angle of projection is (a) 450 (b) 300 (c) cos–1 (3/10) (d) cos ( 3 / 10 ) −1 42. An aeroplane is flying at a constant horizontal velocity of 600 km/hr at an elevation of 6 km towards a point directly above the target on the earth’s surface. At an appropriate time, the pilot releases a ball so that it strikes the target at the earth. The ball will appear to be falling (a) On a parabolic path as seen by pilot in the plane (b) Vertically along a straight path as seen by an observer on the ground near the target (c) On a parabolic path as seen by an observer on the ground near the target (d) On a zig-zag path as seen by pilot in the plane 43. A ball rolls off top of a staircase with a horizontal velocity um/s. If the steps are h metre high and bmere wide, the ball will just hit the edge of nth step if n equals to (a) 2 2 gb hu (b) 2 2 8 gb u (c) 2 2 2 gb hu (d) 2 2 2 hb u g 44. A body is projected horizontally from the top of a tower with initial velocity 18 ms–1 . It hits the ground at angle 45o . What is the vertical component of velocity when it strikes the ground (a) 9 ms–1 (b) 9 2 ms–1 (c) 18 ms–1 (d) 18 2 ms–1 45. A man standing on the roof of a house of height h throws one particle vertically downwards and another particle horizontally with the same velocity u. The ratio of their velocities when they reach the earth’s surface will be (a) 2gh u : u 2 + (b) 1 : 2 (c) 1 : 1 (d) 2gh u : 2gh 2 + 46. A staircase contains three steps each 10 cm high and 20 cm wide. What should be the minimum horizontal velocity of a ball rolling off the uppermost plane so as to hit directly the lowest plane (a) 0.5 m/s (b) 1 m/s (c) 2 m/s (d) 4 m/s 47. An aeroplane moving horizontally with a speed of 720 km/h drops a food packet, while flying at a height of 396.9 m. The time taken by a food packet to reach the ground and its horizontalrange is (Take g = 9.8 m/sec2 ) (a) 3 sec and 2000 m (b) 5 sec and 500 m b h u
(c) 8 sec and 1500 m (d) 9 sec and 1800 m 48. A shell is fired from a gun from the bottom of a hill along its slope. The slope of the hill is  = 30o , and the angle of the barrel to the horizontal  = 60o . The initial velocity v of the shell is 21 m/sec. Then distance of point from the gun at which shell will fall (a) 10 m (b) 20 m (c) 30 m (d) 40 m 49. The maximum range of rifle bullet on the horizontal ground is 6 km its maximum range on an inclined of 300 will be (a) 1 km (b) 2 km (c) 4 km (d) 6 km 50. If a particle moves in a circle describing equal angles in equal times, its velocity vector (a) Remains constant (b) Changes in magnitude (c) Changes in direction (d) Changes both in magnitude and direction 51. Two particles of mass M and m are moving in a circle of radii R and r. If their time-periods are same, what will be the ratio of their linear velocities (a) MR :mr (b) M : m (c) R : r (d) 1 : 1 52. A body is revolving with a uniform speed v in a circle of radius r. The angular acceleration of the body is (a) r v (b) Zero (c) r v 2 along the radius and towards the centre (d) r v 2 along the radius and away from the centre 53. The linear acceleration of a car is 10m/s2 . If the wheels of the car have a diameter of 1m, the angular acceleration of the wheels will be (a) 10 rad/sec2 (b) 20 rad/sec2 (c) 1 rad/sec2 (b) 2 rad/sec2 54. The angular speed of a motor increases from 600 rpm to 1200 rpm in 10 s. What is the angular acceleration of the motor (a) 2 600 − rad sec (b) 2 60 −  rad sec (c) 2 60 − rad sec (d) 2 2 −  rad sec 55. If a cycle wheel of radius 4 m completes one revolution in two seconds. Then acceleration of the cycle will be (a) 2 2  m / s (b) 2 2 2 m / s (c) 2 2 4 m / s (d) 2 8 m/s 56. A stone is tied to one end of a spring 50 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 10 revolutions in 20 s, what is the magnitude of acceleration of the stone (a) 493 cm/sec2 (b) 720 cm/sec2 (c) 860 cm/sec2 (d) 990 cm/sec2 57. A particle moves with a constant speed v along a circular path of radius r and completes the circle in time T. What is the acceleration of the particle (a) mg (b) T 2v (c) T r 2  (d) T v 2  58. If the speed of revolution of a particle on the circumference of a circle and the speed gained in falling through a distance equal to half the radius are equal, then the centripetal acceleration will be (a) 2 g (b) 4 g (c) 3 g (d) g 59. Two cars going round curve with speeds one at 90 km/h and other at 15 km/h. Each car experiences same acceleration. The radii of curves are in the ratio of (a) 4 : 1 (b) 2 : 1 (c) 16 : 1 (d) 36 : 1 60. A wheel of radius 0.20m is accelerated from rest with an angular acceleration of 2 1 rad /s . After a rotation of o 90 the radial acceleration of a particle on its rim will be (a) 2  m / s (b) 2 0.5  m / s (c) 2 2.0 m / s (d) 2 0.2  m /s 61. A ball of mass 0.1 kg is whirled in a horizontal circle of radius 1 m by means of a string at an initial speed of 10 r.p.m. Keeping the radius constant, the tension in the string is reduced to one quarter of its initial value. The new speed is (a) 5 r.p.m. (b) 10r.p.m. (c) 20r.p.m (d) 14r.p.m. 62. A cylindrical vessel partially filled with water is rotated about its vertical central axis. It’s surface will (a) Rise equally (b) Rise from the sides (c) Rise from the middle (d) Lowered equally 63. A proton of mass 1.6 × 10–27kg goes round in a circular orbit of radius 0.10 m under a centripetal force of 4 × 10–13N. then the frequency of revolution of the proton is about (a) 0.08 × 108 cyclespersec (b) 4 × 108 cyclesper sec (c) 8 × 108 cyclespersec (d) 12 × 108 cyclespersec 64. Three identical particles are joined together by a thread as shown in figure. All the three particles are moving in a horizontal plane. If the velocity of the outermost particle is v0, then the ratio of tensions in the three sections of the string is [PMT 2003]