NEET AIPMT Physics Chapter Wise Solutions - Motion in a Plane

NEET AIPMT Physics Chapter Wise Solutions – Motion in a Plane

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NEET AIPMT Physics Chapter Wise Solutions Chemistry Biology

1. If vectors $\bar { A }$ = coswt $\hat { i }$ + sinwt $\hat { j }$ and $\bar { B }$ = cos $\frac { wt }{ 2 }$ $\hat { i }$ + sin $\frac { wt }{ 2 }$ $\hat { j }$ are functions of time, then the value of 7 at which they are orthogonal to each other is

2. The position vector of a particle R as a function of time is given by $\xrightarrow { R }$ = 4sin(2πt) $\hat { i }$ + 4cos(2πt) $\hat { j }$ y Where R is in meters, 7 is in seconds and 7 and j denote unit vectors along x-and j’-directions, respectively. Which one of the following statements is wrong for the motion of particle?
(a) Magnitude of the velocity of particle is 8 meter/second.
(b) Path of the particle is a circle of radius 4 meter.
(c) Acceleration vector is along – $\xrightarrow { R }$
(d) Magnitude of acceleration vector is R where v is $\frac { V2 }{ R }$ the velocity of particle. (AIPMT 2015)

3. A ship A is moving Westwards with a speed of 10 km h^-1and a ship B 100 km South of A, is moving Northwards with a speed of 10 kmh^-1.The time after which the distance between them becomes shortest, is
(a) 5 $\sqrt { 2 }$ h
(b) 10 $\sqrt { 2 }$ h
(c) 0h
(d) 5 h (AIPMT 2015, Cancelled)

4. A projectile is fired from the surface of the earth with a velocity of 5 m s^-1and angle 0 with the horizontal. Another projectile fired from another planet with a velocity of 3 ms^-1at the same angle follows a trajectory which is identical with the trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet is (in m s^-2) is (Given g = 9.8 m s^-2)
(a) 3.5
(b) 5.9
(c) 16.3
(d) 110.8 (AIPMT 2014)

5. A particle is moving such that its position coordinates (x, y) are (2 m, 3 m) at time t=0, (6 m, 7 m) at time t = 2 s and (13 in, 14 m) at time t = 5 s. Average velocity vector (vav) from t = 0 to t = 5 s is

6. The velocity of a projectile at the initial point A is (2 $\hat { i }$ + 3 $\hat { j }$ ) m/s. It’s velocity (in m/s) at point B is

7. Vectors $\bar { A }$ , $\bar { B }$ and $\bar { C }$ are such that $\bar { A }$ . $\bar { B }$ = 0 and $\bar { A }$ . $\bar { B}$ = 0. Then the vector parallel to A is
(a) $\bar { A }$ x $\bar { B }$
(b) $\bar { B }$ + $\bar { C }$
(c) $\bar { B }$ x $\bar { C }$
(d) $\bar { B }$ and $\bar { C }$ (Karnataka NEET 2013)

8. The horizontal range and the maximum height of a projectile are equal. The angle of projection of the projectile is

9. A particle has initial velocity (2) + 3/) and acceleration (0.37 + 0.2/). The magnitude of velocity after 10 seconds will be
(a) 9 $\sqrt { 2 }$ units
(b) 5 $\sqrt { 2 }$ units
(c) 5 units
(d) 9 units (Prelims 2012)

10. A particle moves in a circle of radius 5 cm with constant speed and time period 0.2tt s. The acceleration of the particle is
(a) 15 m/s²
(b) 25 m/s²
(c) 36 m/s²
(d) 5 m/s² (Prelims 2011)

11. A missile is fired for maximum range with an initial velocity of 20 m/s. Ifg = 10 m/s², the range of the missile is
(a) 40 m
(b) 50 m
(c) 60 m
(d) 20 m (Prelims 2011 )

12. A body is moving with velocity 30 m/s towards east. After 10 seconds its velocity becomes 40 m/s towards north. The average acceleration of the body is
(a) 1 m/s²
(b) 7 m/s²
(c) $\sqrt { 7 }$ m/s²
(d) 5 m/s²(Prelims 2011)

13. A projectile is fired at an angle of 45° with the horizontal. Elevation angle of the projectile at its highest point as seen from the point of projection, is

14. A particle has initial velocity (3 $\hat { i }$ + 4 $\hat { J }$ ) and has acceleration (0.4 $\hat { i }$ +0.3 $\hat { J }$ ). Its speed after 10 s is
(a) 7 units
(b) 7 $\sqrt { 2 }$ units
(c) 8.5 units
(d) 10 units (Prelims 2010)

15. Six vectors, $\bar { a }$ through $\bar { f }$ have the magnitudes and directions indicated in the figure. Which of the following statements is true?

16. TTie speed of a projectile at its maximum height is half of its initial speed. The angle of projection is
(a) 60°
(b) 15°
(c) 30°
(d) 45° (Mains 2010)

17. A particle moves in x-y plane according to rule x = asinωt and y = acosωt. The particle follows
(a) an elliptical path
(b) a circular path
(c) a parabolic path
(d) a straight line path inclined equally to x and y-axes (Mains 2010)

18. A particle shows distance – time curve as given in this figure. The maximum instantaneous velocity of the particle is around the point

(a) D
(b) A
(c) B
(d) C

19. A particle of mass m is projected with velocity v making an angle of 45° with the horizontal. When the particle lands on the level ground the magnitude of the change in its momentum will be

20. $\bar { A }$ and $\bar { B }$ are two vectors and 0 is the angle between them, if | $\bar { A }$ x $\bar { B }$ | = $\sqrt { 3 }$ ( $\bar { A }$ . $\bar { B }$ ), the value of 0 is t
(a) 45°
(b) 30°
(c) 90°
(d) 60°. (2007)

21. A particle starting from the origin (0, 0) moves in a straight line in the (x,y) plane. Its coordinates at a later time are ( $\sqrt { 3 }$ ,3) . The path of the particle makes with the x-axis an angle of
(a) 45°
(b) 60°
(c) 0°
(d) 30°. (2007)

22 . A tube of length L is filled completely with an incompressible liquid of mass M and closed at both the ends. The tube is then rotated in a horizontal plane about one of its ends with a uniform angular velocity to. The force exerted by the liquid at the other end is

23. For angles of projection of a projectile at angle (45° – 0) and (45° + 0), the horizontal range ’ described by the projectile are in the ratio of
(a) 2 : 1
(b) 1 : 1
(c) 2:3
(d) 1 :2. (2006)

24. The vectors $\bar { A}$ and $\bar { B}$ are such that \ $\bar { A}$ + $\bar { B}$ \ = \ $\bar { A}$ – $\bar { B}$ |. The angle between the two vectors is
(a) 45°
(b) 90°
(c) 60°
(d) 75°. (2006, 1996, 91)
horizontal circle with a constant speed. If the stone makes

25. Two boys are standing at the ends A and B of a ground where AB = a. The boy at B starts running in a direction perpendicular to AB with velocity V1. The boy at A starts running simultaneously with velocity v and catches the other in a time t, where t is

26. A stone tied to the end of a string of 1 m long is whirled in a horizontal circle with a constant speed. If the stone makes 22 revolutions in 44 seconds, what is the magnitude and direction of acceleration of the stone?
(a) π² ms^-2 and direction along the radius towards the centre
(b) π²ms^-2 and direction along the radius away from the centre
(c) π² ms^-2 and direction along the tangent to the circle
(d) π²/4 ms^-2 and direction along the radius towards the centre. (2005)

27. If the angle between the vectors $\bar { A}$ and $\bar { B}$ is θ,the value of the product ( $\bar{ B}$ x $\bar { A}$ ). $\bar { A}$ is equal to
(a) BA²sinθ
(b) BA4²cosθ
(c) BA²2sinθcosθ
(d) zero. (2005, 1989)

28. If a vector 2 $\hat { i }$ +3 $\hat { j }$ + 8 $\hat { k }$ is perpendicular to the vector 4 $\hat { j }$ – 4 $\hat { i }$ + a $\hat { k }$ , then the value of a is
(a) 1/2
(b) -1/2
(c) 1
(d) -1. (2005)

29. If | $\bar { A}$ x $\bar { B}$ |= $\sqrt { 3 }$ $\bar { A}$ . $\bar { B}$ then the value of | $\bar { A}$ + $\bar { B}$ |

30. The vector sum of two forces is perpendicular to their vector differences. In that case, the forces
(a) are equal to each other
(b) are equal to each other in magnitude
(c) are not equal to each other in magnitude
(d) cannot be predicted. (2003)

31. A particle moves along a circle of radius m with constant tangential acceleration. If the velocity of the particle is 80 m/s at the end of the second revolution after motion has begun, the tangential acceleration is
(a) 40 m/s²
(b) 6407rm/s²
(c) 1607t m/s²
(d) 407t m/s² (2003)

32. A particle A is dropped from a height and another particle B is projected in horizontal direction with speed of 5 m/sec from the same height then correct statement is:
(a) particle’A will reach at gfound first with respect to particle B
(b) particle B will reach at ground first with respect to particle A
(c) both particles will reach at ground simultaneously
(d) both particles will reach at ground with same speed. (2002)

33. An object of mass 3 kg is at rest. Now a force of $\bar { F }$ = 6t² $\hat { i }$ + 4t $\hat { j }$ is applied on the object then velocity of object at t = 3 sec. is

34. If | $\bar { A }$ + $\bar { B }$ |= \ $\bar { A }$ \ + \ $\bar { B }$ \ then angle between A and B will be
(a) 90°
(b) 120°
(c) 0°
(d) 60°. (2001)

35. Two particles having mass M and m are moving in a circular path having radius R and r. If their time period are same then the ratio of angular

36. The width of river is 1 km. The velocity of boat is 5 km/hr. The boat covered the width of river in shortest time 15 min. Then the velocity of river stream is

37. Two projectiles of same mass and with same velocity are thrown at an angle 60° and 30° with the horizontal, then which will remain same
(a) time of flight
(b) range of projectile
(c) maximum height acquired
(d) all of them. (2000)

38. A man is slipping on a ffictionless inclinecTplane and a bag falls down from the same height. Then the velocity of both is related as
(a) V_B>Vm
(b)V_B < Vm
(c) V_B = Vm
(d) V_B and Vm can’t be related. (2000)

39. A 500 kg car takes a round turn of radius 50 m with a velocity of 36 km/hr. The centripetal force is
(a) 1000 N
(b) 750 N
(c) 250 N
(d) 1200 N (1999)

40. A person aiming to reach exactly opposite point on the bank of a stream is swimming with a speed of 0.5 m/s at an angle of 120° with the direction of flow of water. The speed of water in the stream, is
(a) 0.25 m/s
(b) 0.5 m/s
(c) 1.0 m/s
(d) 0.433 m/s (1999)

41. Two racing cars of masses m1 and m2 are moving in circles of radii r1 and r2 respectively. Their speeds are such that each makes a complete circle in the same time t. The ratio of the angular speeds of the first to the second car is
(a) r1 : r2
(b) m1 : m2
(c) 1:1
(d) m1 m2 : r r2 (1999)

42. If a unit vector is represented by 0.5 $\hat { i }$ -0.8 $\hat { j }$ + c $\hat { k }$ then the value of c is

43. What is the value of linear velocity, if $\bar { r }$ =3 $\hat { i }$ -4 $\hat { j }$ + $\hat { k }$ and to $\bar { w }$ = 5 $\hat { i }$ – 6 $\hat { j }$ + 6 $\hat { k }$ ?

44. Two particles A and B are connected by a rigid rod AB. The rod slides along perpendicular rails as shown here. The velocity of A to the left is 10 m/s. What is the velocity of B when angle a = 60°?

(a) 10 m/s
(b) 9.8 m/s
(c) 5.8 m/s
(d) 17.3 m/s. (1998)

45. A ball of mass 0.25 kg attached to the end of a string of length 1.96 m is moving in a horizontal circle. The string will break if the tension is more than 25 N. What is the maximum speed with which the ball can be moved?
(a) 5 m/s
(b) 3 m/s
(c) 14 m/s
(d) 3.92 m/s. (1998)

46. Identify the vector quantity among the following
(a) distance
(b) angular momentum
(c) heat
(d) energy. (1997)

47. A body is whirled in a horizontal circle of radius 20 cm. It has an angular velocity of 10 rad/s. What is its linear velocity at any point on circular path?
(a) 20 m/s
(b) $\sqrt { 2 }$ m/s
(c) 10 m/s
(d) 2 m/s. (1996)

48. The position vector of a particle is $\bar { r }$ =(acoswt) $\hat { i }$ +(asinwt) $\hat { j }$ . The velocity of the particle is
(a) directed towards the origin
(b) directed away from the origin
(c) parallel to the position vector
(d) perpendicular to the position vector. (1995)

49. The angular speed of a flywheel making 120 revolutions/minute is
(a) 4π rad/s
(b) 4π² rad/s
(c) πrad/s
(d) 2π rad/s. (1995)

50. The angle between the two vectors $\bar { A }$ = 3 $\hat { i }$ +4 $\hat { j }$ + 5 $\hat { k }$ and $\bar { B }$ = 3 $\hat { i }$ +4 $\hat { j }$ -5 $\hat { k }$ will be
(a) 90°
(b) 180°
(c) zero
(d) 45°. (1994)

51. A boat is sent across a river with a velocity of 8kmh^-1. If the resultant velocity of boat is 10 kmh^-1, then velocity of river is
(a) 12.8 kmh^-1
(b) 6 kmh^-1
(c) 8 kmh^-1
(d) 10 kmh^-1 (1994, 93)

52. If a body A of mass M is thrown with velocity v at an angle of 30° to the horizontal and another body B of the same mass is thrown with the same speed at an angle of 60° to the horizontal, the ratio of horizontal range of A to B will be
(a) 1:3
(b) 1:1
(c) 1: $\sqrt { 3}$
(d) $\sqrt { 3 }$ :l. (1992, 90)

53. The resultant of $\bar { A }$ xO will be equal to
(a) zero
(b) A
(c) zero vector
(d) unit vector. (1992)

54. When milk is churned, cream gets seperated due to
(a) centripetal force
(b) centrifugal force
(c) frictional force
(d) gravitational force (1991)

55. An electric fan has blades of length 30 cm measured from the axis of rotation. If the fan is rotating at 120 rpm, the acceleration of a point on the tip of the blade is
(a) 1600 ms^-2
(b) 47.4 ms^-2
(c) 23.7 ms^-2
(d) 50.55 ms^-2 (1990)

56. The maximum range of a gun of horizontal terrain is 16 km. Ifg = 10 ms^-2 , then muzzle velocity of a shell must be
(a) 160 ms^-1
(b) 20o $\sqrt { 2 }$ ms^-1
(c) 400 ms^-1
(d) 800 ms^-1 (1990)

57. A bus is moving on a straight road towards north with a uniform speed of 50 km/hour then it turns left through 90°. If the speed remains unchanged after turning, the increase in the velocity of bus in the turning process is
(a) 70.7 km/hr along south-west direction
(b) zero
(c) 50 km/hr along west
(d) 70.7 km/hr along north-west direction (1989)

58. The magnitude of vectors $\bar { A }$ , $\bar { B }$ and $\bar { C }$ are 3, 4 and 5 units respectively. If $\bar { A }$ + $\bar { B }$ = $\bar { C }$ , the angle between $\bar { A }$ and $\bar { B}$ is
(a) π/2
(b) cos^-1(0.6)
(c) tan^-1(7/5)
(d) π/4. (1988)

59. A train of 150 metre length is going towards north direction at a speed of 10 m/s. A parrot flies at the speed of 5 m/s towards south direction parallel to the railways track. The time taken by the parrot to cross the train is
(a) 12 sec
(b) 8 sec
(c) 15 sec
(d) 10 sec. (1988)

NEET AIPMT Physics Chapter Wise Solutions – Motion in a Plane

NEET AIPMT Physics Chapter Wise Solutions – Motion in a Plane

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