## NEET AIPMT Physics Chapter Wise Solutions – Motion in a Plane

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NEET AIPMT Physics Chapter Wise SolutionsChemistryBiology

**1. If vectors = coswt + sinwt and = cos + sin 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 = 4sin(2πt) + 4cos(2πt) 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 –

(d) Magnitude of acceleration vector is R where v is the velocity of particle. **(AIPMT 2015)**

**3. A ship A is moving Westwards with a speed of 10 km h**^{-1 }**and 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) 5h

(b) 10 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 ^{-1 }and angle 0 with the horizontal. Another projectile fired from another planet with a velocity of 3 ms^{-1 }at 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 + 3 ) m/s. It’s velocity (in m/s) at point B is**

**7. Vectors , and are such that . = 0 and . = 0. Then the vector parallel to A is**

(a) x

(b) +

(c) ** ** x

(d) and **(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 units

(b) 5 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/s^{2}

(b) 25 m/s^{2}

(c) 36 m/s^{2}

(d) 5 m/s^{2} (Prelims 2011)

**11. A missile is fired for maximum range with an initial velocity of 20 m/s. Ifg = 10 m/s ^{2}, 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/s^{2}

(b) 7 m/s^{2}

(c) m/s^{2}

(d) 5 m/s^{2}**(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 + 4 ) and has acceleration (0.4 +0.3 ). Its speed after 10 s is
(a) 7 units
(b) 7 units
(c) 8.5 units
(d) 10 units (Prelims 2010)**

**15. Six vectors, through 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. and are two vectors and 0 is the angle between them, if | x | = (. ), 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 (,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 and are such that \ + \ = \– |. 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) π^{2} ms^{-2} and direction along the radius towards the centre

(b) π^{2}ms^{-2} and direction along the radius away from the centre

(c) π^{2} ms^{-2} and direction along the tangent to the circle

(d) π^{2}/4 ms^{-2} and direction along the radius towards the centre.** (2005)**

**27. If the angle between the vectors and is θ,the value of the product (x). is equal to
**(a) BA

^{2}sinθ

(b) BA4

^{2}cosθ

(c) BA

^{2}2sinθcosθ

(d) zero. (2005, 1989)

**28. If a vector 2 +3 + 8 is perpendicular to the vector 4 – 4 + a , then the value of a is**

(a) 1/2

(b) -1/2

(c) 1

(d) -1. **(2005)**

**29. If | x** ** |= . then the value of | + | **

**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/s^{2}

(b) 6407rm/s^{2}

(c) 1607t m/s^{2}

(d) 407t m/s^{2} **(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 = 6t ^{2} + 4t is applied on the object then velocity of object at t = 3 sec. is**

**34. If |+ |= \\ + \\ 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 -0.8 + c then the value of c is**

**43. What is the value of linear velocity, if =3 -4 + and to = 5 – 6 + 6 ?**

**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) m/s

(c) 10 m/s

(d) 2 m/s. **(1996)**

**48. The position vector of a particle is =(acoswt)+(asinwt) . 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) 4π^{2} rad/s

(c) πrad/s

(d) 2π rad/s. **(1995)**

**50. The angle between the two vectors = 3+4+ 5 and = 3 +4-5 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:

(d) :l.** (1992, 90)**

**53. The resultant of 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) 20oms

^{-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 , and are 3, 4 and 5 units respectively. If + = , the angle between and 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)**

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