Title 04. MOtion in a plane Medium.pdf ✅

1. A river is flowing due east with a speed 1 3ms − . A swimmer can swim in still water at a speed of 1 4ms − . If swimmer starts swimming due north, then the resultant velocity of the swimmer is (a) 1 3ms − (b) 1 5ms − (c) 1 7ms − (d) 1 2ms − 2. The driver of a car moving towards a rocket launching pad with a speed of 1 6ms − observed that the rocket is moving with speed of 1 10ms − . The upward speed of the rocket as seen by the stationary observer is nearly (a) 1 4ms − (b) 1 6ms − (c) 1 8ms − (d) 1 11ms − 3. A bomb is released by a horizontal flying aeroplane. The trajectory of the bomb is (a) A parabola (b) A straight line (c) A circle (d) A hyperbola 4. In case of a projectile motion, what is the angle between the velocity and acceleration at the highest point? (a) o 0 (b) o 45 (c) o 90 (d) o 180 5. A cricketer can throw a ball to a maximum horizontal distance of 100 m. How high above the ground can the cricketer throw the same ball? (a) 100 m (b) 50 m (c) 25 m (d) 5 m 6. Which of the following is true regarding projectile motion? (a) Horizontal velocity of projectile is constant (b) Vertical velocity of projectile is constant (c) Acceleration is not constant (d) Momentum is constant 7. An aeroplane flying horizontally with a speed of 360 km-1 releases a bomb at a height of 490 m from the ground. If g = 9.8 m s-2 , it will strike the ground at (a) 10 km (b) 100 km (c) 1 km (d) 16 km 8. Galileo writes that for angles of projection of a projectile at angles ( +  o 45 ) and ( − o 45 ), the horizontal ranges described by the projectile are in the ratio of ( o if   45 ) (a) 2 : 1 (b) 1 : 2 (c) 1 : 1 (d) 2 : 3 9. The ceiling of a hall is 40 m high. For maximum horizontal distance, the angle at which the ball may be thrown with a speed of 56 m s-1 without hitting the ceiling of the hall is (a) 0 25 (b) o 30 (c) o 45 (d) o 60 10. Two projectiles are fired from the same point with the same speed at angles of projection o 60 and o 30 respectively. Which one of the following is true? (a) Their range will be the same (b) Their maximum height will be the same (c) Their velocity at the highest point will be the same (d) Their time of flight will be the same 11. Two balls are projected at an angle  and ( − o 90 ) to the horizontal with the same speed. The ration of their maximum vertical heights is (a) 1 : 1 (b) tan  :1 (c) 1: tan  (d) tan :1 2  12. If R and H represent horizontal range and maximum height of the projectile, then the angle of projection with the horizontal is (a)      −  R H tan 1 (b)      −  R 2H tan 1 (c)      −  R 4H tan 1 (d)      −  H 4R tan 1 13. The relation between the time of flight of projectile Tf and the time to reach the maximum height m t is (a) f m T = 2t (b) f m T = t (c) 2 t T m f = (d) T 2(t ) f = m 14. When air resistance is taken into account while dealing with the motion of the projectile which of the following properties of the projectile, shows an increase? (a) Range (b) Maximum height (c) Speed at which it strikes the ground (d) The angle at which the projectile strikes the ground 15. Two particles are projected simultaneously in the same vertical plane, from the same point, both with different speeds and at different angles with horizontal. The path followed by one, as seen by the other, is (a) A vertical line (b) A parabola (d) A hyperbola (d) A straight line making a constant angle ( o  90 ) with horizontal 16. Centripetal acceleration is (a) A constant vector (b) A constant scalar (c) A magnitude changing vector (d) Not a constant vector 17. A cyclist is riding with a speed of 27 km h_1 . As he approaches a circular turn on the road of radius 80 m, he applies brakes and reduces his speed at the constant rate of 0.05 m s-1 every second. The net acceleration of the cyclist on the circular turn is (a) 2 0.68ms − ( 2 0.68m/s ) (b) 2 0.86ms − ( 2 0.86m/s ) (c) 2 0.56ms − ( 2 0.56m/s ) (d) 2 0.76ms − ( 2 0.76m/s ) 18. A particle is moving on a circular path of radius r with uniform speed v. What is the displacement of the particle after it has described an angle of o 60 ? (a) r 2 (b) r 3 (c) r (d) 2r 19. Velocity vector and acceleration vector in a uniform circular motion are related as
(a) Both in the same related as (b) Perpendicular to each other (c) Both in opposite direction (d) Not related to each other 20. If the angle between the vectors AandB   is  , the value of the product ( B A    ). A  is equal to (a) BA cos 2 (b) BA sin  2 (c) BA sin cos 2 (d) Zero 21. If unit vectors B ˆ A and ˆ are inclined at an angle  , then B| A ˆ ˆ | − is (a) 2 2sin  (b) 2 2cos  (c) 2 2 tan  (d) 2 2cot  22. The angle between j ˆ i A ˆ = +  and j ˆ i B ˆ = −  is (a) o 45 (b) o 90 (c) o − 45 (d) o 180 23. Which one of the following statements is true? (a) A scalar quantity is the one that is conserved in a process (b) A scalar quantity is the one that can never take negative values (c) A scalar quantity is the one that does not vary from one point to another in space (d) A scalar quantity has the same value for observers 24. Figure shows the orientation of two vectors u  and v  in the xy plane. If j ˆ i b ˆ u = a +  and j ˆ i q ˆ v = p +  . Which of the following is correct? (a) A and p are positive while b and q are negative (b) A, p and b are positive while q is negative (c) A, q and b are positive while p is negative (d) A, b, p and q are all positive 25. The position of a particle is given by k ˆ j 5 ˆ i 2t ˆ r = 3t + +  , where t is in seconds and the coefficients have the proper units for r  to be in metres. The direction of velocity of the particle at t = 1 s is (a) o 53 with x-axis (b) o 37 with x-axis (c) o 30 with y-axis (d) o 60 with y-axis 26. On an open ground, a motorist follows a track that turns to his left by an angle of o 60 after every 500 m. Starting from a given turn, the displacement of the motorist at the third turn is (a) 500 m (b) 500 3m (c) 1000 m (d) 1000 3m 27. For any arbitrary motion in space, which of the following relations is true? (a) [v(t ) v(t )] 2 1 vaverage 1 2    = + (b) 2 1 2 1 average t t r(t ) r(t ) v − − =    (c) v(t) v(0) at    = + (d) 2 at 2 1 r(t) r(0) v(0)t     = + + 28. A fighter plane is flying horizontally at an altitude of 1.5 km with speed 720 km h-1 . At what angle of sight (w.r.t. horizontal) when the target is seen, should the pilot drop the bomb in order to attack the target? (Take g 10ms ,tan 23 0.43 2 o = = − ) (a) o 23 (b) o 32 (c) o 12 (d) o 42 29. Four girls skating on circular ice ground of radius 200 m start from a point P on the edge of the ground and reach a point Q diametrically opposite to P following different paths as shown in figure. For which girl displacement is equal to the actual length of path skate? (a) A (b) B (c) C (d) D 30. A particle starts from origin at t = 0 with a velocity 1 i ms ˆ 5 − and moves in x-y plane under the action of force which produces a constant acceleration of 2 jms ˆ i 2 ˆ 3 − + . The y- coordinate of the particle at the instant when its x-coordinate is 84 m is (a) 12 m (b) 24 m (c) 36 m (d) 48 m 31. A river is flowing from west to east with a speed 1 5 m s − . A swimmer can swim in still water at a speed of 1 10 m s − . If he wants to start from point A on south bank and reach opposite point B on north bank, in what direction should he swim? (a) o 30 east of north (b) o 60 east of north (c) o 30 west of north (d) o 60 west of north 32. Rain is falling vertically with a speed of 30 m s-1 . A woman rides a bicycle with a speed of 12 m s-1 in east to west direction. In which direction she should hold her umbrella? (a) At an angle of      −  5 2 tan 1 with the vertical towards the east
(b) At angle of      −  5 2 tan 1 with the vertical towards the west (c) At angle of      −  2 5 tan 1 with the vertical towards the east (d) At angle of      −  2 5 tan 1 with the vertical towards the west 33. A girl riding a bicycle with a speed of 5 m s-1 towards north direction, observes rain falling vertically down. If she increases her speed to 10 m s-1 , rain appears to meet her at o 45 to the vertical. What is the speed of the rain? (a) 1 5 2 m s − (b) 1 5 m s − (c) 1 10 2 m s − (d) 1 10 m s − 34. Suppose that two objects A and B are moving with velocities A B v and v   (each with respect ot some common frame of reference). Let vAB  represent the velocity of A with respect to B. Then (a) vAB + vBA = 0   (b) vAB − vBA = 0   (c) vAB vA vB    = + (d) | v | | v | AB BA    35. A cricketer can throw a ball to a maximum horizontal distance of 100m. With the same speed how much high above the ground can the cricketer throw the same ball? (a) 50 m (b) 100 m (c) 150 m (d) 200 m 36. A particle is projected in air at an angle  to a surface which itself is inclined at an angle  to the horizontal. Then distance L is equal to (a)    +  2 2 g cos 2u sin cos( ) (b)    +  2 2 gcos 2u sin cos( ) (c)    +  2 2 gcos 2u sin cos( ) (d)    +  2 2 gcos 2u sin cos( ) 37. A hiker stands on the edge of a cliff 490 m above the ground and throw a stone horizontally with a speed of 15 m s-1 . The time taken by the stone to reach the ground is (a) 5 s (b) 10 s (c) 12 s (d) 15 s 38. A cricketer ball is thrown at a speed of 30 m s-1 a direction o 30 above the horizontal. The time taken by the ball to return to the same level is. (Take g = 10 m s-2 ) (a) 2 s (b) 3 s (c) 4 s (d) 5 s 39. The equations of motion of a projectile are given by x = 36t m and 2y = 96t – 9.8t2 m. The angle of projection is (a)      −  5 4 sin 1 (b)      −  5 3 sin 1 (c)      −  3 4 sin 1 (d)      −  4 3 sin 1 40. The equation of motion of a projectile is 2 y = ax − bx , where a and b are constants of motion. Match the quantities of Column I with the relations of Column II. Column I Column II (A) The initial velocity of projection (p) b a (B) The horizontal range of projectile (q) bg 2 a (C) The maximum vertical height attained by projectile (r) 4b a 2 (D) The time of flight of projectile (s) 2 b g(1 a ) 2 + (a) A – p, B – q, C – r, D – s (b) A – s, B – p, C – q, D – r (c) A – s, B – p, C – r, D – q (d) A – p, B – s, C – r, D – q 41. Two particles are projected in air with speed u at angles 1 and 2 (both acute) to the horizontal, respectively. If the height reached by the first particle is greater than that of the second, then which one of the following is correct. (a) 1  2 (b) 1 = 2 (c) T1  T2 (d) T1 = T2 Where T1 and T2 are the time of flight 42. If a body is projected with an angle  to the horizontal, then (a) Its velocity is always perpendicular to its acceleration (b) Its velocity becomes zero at its maximum height (c) Its velocity makes zero angle with the horizontal at its maximum height (d) The body just before hitting the ground, the direction of velocity coincides with the acceleration 43. A ball is thrown form the top of a tower with an initial velocity of 10 m s-1 at an angle of o 30 with the horizontal. If it hits the ground of a distance of 17.3 m from the back of the tower, the height of the tower is (Take g = 10 m s-2 ). (a) 5 m (b) 20 m (c) 15 m (d) 10 m 44. The speed of a projectile at its maximum height is 2 3 times its initial speed. If the range of the projectile is P times the maximum height attained by it, then P equals (a) 3 4 (b) 3 4 (c) 4 3 (d) 4 3 45. Four bodies A, B, C and D are projected with equal velocities having angles of projection o o o 15 ,30 ,45 and o 60 with the horizontal respectively. The body having the shortest range is (a) A (b) B (c) C (d) D
46. A player kicks a ball at a speed of 20 m s-1 so that its horizontal range is maximum. Another player 24 m away in the direction of kick starts running in the same direction at the same instant of hit. If he has to catch the ball jusy before it reaches the ground, he should run with a velocity equal to (Take g = 10 m s-1 ) (a) 1 2 2 m s − (b) 1 4 2 m s − (c) 1 6 2 ms − (d) 1 10 2 m s − 47. A cyclist starts from centre O of a circular park of radius 1 km and moves along the path OPRQO as shown in figure. If he maintains constant speed of 10 m s-1 , what is his acceleration at point R? (a) 10 m s-2 (10 m/s2 ) (b) 0.1 m s-2 (0.1 m/s2 ) (c) 0.01 m s-2 (0.01 m/s2 ) (d) 1 m s_2 (1 m/s2 ) 48. A ball is thrown from a roof top at an angle of o 45 above the horizontal. It hits the grount a few seconds later. The ball has the smallest speed during its motion when (a) It is at the highest point (b) It is at the point of projection (c) It hits the ground (d) Both (b) and (c) 49. A body executing uniform circular motion has at any instant its velocity vector and acceleration vector (a) Along the same direction (b) In opposite direction (c) Normal to each other (d) Not related to each other 50. A stone tied to the end of a string 100 cm long is whirled in a horizontal circle with a constant speed. If the stone makes 14 revolutions in 22 s, then the acceleration of the stone is (a) 2 16ms − ( 2 16m/s ) (b) 2 4ms − ( 2 4m/s ) (c) 2 12ms − ( 2 12m/s ) (d) 2 8ms − ( 2 8m/s ) 51. A cyclist starts from the centre O of a circular park of radius 1 km, reaches the edge P of the park, then cycles along the circumference and returns to the centre along QO as shown in the figure. If the round trip takes ten minutes, the net displacement and average speed of the cyclist (in metre and kilometer per hour) is (a) 0, 1 (b) ,0 2  + 4 (c) 2 4 21.4,  + (d) 0, 21.4 52. For a particle performing uniform circular motion, choose the incorrect statement from the following. (a) Magnitude of particle velocity (speed) remains constant (b) Particle velocity remains directed perpendicular to radius vector (c) Direction of acceleration keeps changing as particle moves (d) Magnitude of acceleration does not remain constant 53. What is approximately the centripetal acceleration (in units of acceleration due to gravity on earth, g = 10 m s-2 ) of an air-craft flying at a speed of 1 400 m s − through a circular arc of radius 0.6 km? (a) 26.7 (b) 16.9 (c) 13.5 (d) 30.2 54. An insect trapped in a circular groove of radius 12 cm moves along the groove steadily and completes 7 revolutions in 100 s. The linear speed of the insect is (a) 1 4.3 cm s − (4.3 cm/s) (b) 1 5.3 cm s − (5.3 cm/s) (c) 1 6.3 cm s − (6.3 cm/s) (d) 1 7.3 cm s − (7.3 cm/s) 55. Which of the following statements is incorrect? (a) In one dimension motion, the velocity and the acceleration of an object are always along the same line (b) In two or three dimensions, the angle between velocity and acceleration vectors may have any value between o 0 and o 180 (c) The kinematice equations for uniform acceleration can be applied in case of a uniform cirucular motion (d) The resultant acceleration of an object in circular motion is towards the centre only if the speed is constant 56. An aircraft is flying at a height of 3400 m above the ground. It the angle subtended at a ground observation point by the aircraft positions 10 s apart is o 30 , then the speed of the aircraft is (a) 1 10.8 m s − (10.8 m/s) (b) 1 1963 m s − (1963 m/s) (c) 1 108 m s − (108 m/s) (d) 1 196.3 m s − (196.3 m/s) 57. A body moves 6 m north, 8 m east and 10 m vertically upwards, the resultant displacement from its initial position is (a) 10 2 m (b) 10 m (c) m 2 10 (d) 20 m 58. A man wants to reach from A to the opposite corner of the square C (Figure). The sides of the square are 100 m each. A central square of 50 m × 50 m is filed with sand. Outside this square, he can walk at a speed 1 1 m s . In the central square, he can walk only at a speed of 1 v m s − (v < A). What is smallest value of v for which he can reach faster via a straight path through the sand than any path in the square outside the sand? (a) 1 0.18 m s − ( 0.18 m/s ) (b) 1 0.81 m s − ( 0.81 m/s ) (c) 1 0.5 m s − ( 0.5 m/s)