Chapter #04 Motion in two Dimension

CHAPTER No. 4 MOTION IN TWO DIMENSIONS 1. An object launched in space having no driving power in an arbitrary direction is called: a) Rocket b) Bullet c) Airship d) Projectile 2. The path of a projectile is called its: a) Curve b) Time of action c) Orbit d) Trajectory 3. An object is thrown in the air with an initial velocity Vi and making an angle  with the surface of the The vertical component of its velocity after time t is given by: a) Vi cos  b) Vi cos  - gt c) Vi sin  - gt d) Vi tan  - gt The velocity V of a projectile can be found by the expression: ˆ ˆ ˆ ˆ a) V = Vi cos  i + (Vi sin  - gt) j b) V = (Vi cos  -gt) i + (Vi sin  - gt) j ˆ ˆ ˆ ˆ c) V = (Vi cos  -gt) i + (Vi sin  - gt) j d) V = Vi cos  i + Vi sin  j 5. The angle  that the projectile makes with the horizontal at any time t during its flight is given by:  Vi cos   gt   Vi  gt      Vi sin   V cos   a)  = tan-1  b)  = tan-1  i  Vi sin     V cos   gt  c)  = tan-1  i d) None of the above 6. In projectile motion, the acceleration in the vertical direction: a) Remains constant b) Varies with time c) Is zero d) Is taken as positive 7. The horizontal component of velocity of a projectile: a) Increases with time b) Decreases with time c) Is uniform d) Is taken negative 8. The vertical component of velocity of a projectile: a) Decreases during upward motion and increases during downward motion Increases during upward motion and decreases during downward motion c) Increases during both upward and downward motions d) Decreases during both upward and downward motions 9. The vertical component of acceleration of a projectile: a) Is less than the gravitational acceleration b) Is equal to the gravitational acceleration c) Is more than the gravitational acceleration d) Has no relation with the gravitational acceleration 10. The path described by a projectile represents a: a) Hyperbola b) Parabola c) Straight line d) Circle 11. The relation between the x and y-components is given by: a) y = ax2 - bx b) y = ax + bx2 2 c) y = ax – bx d) y = bx – ax2 12. The time taken by a projectile to reach its maximum height is: Vi cos  Vi sin  g g a) t  = b) t  = Vi g g sin  V sin  c) t  = d) t  = i 13. The maximum height attained by a projectile is: C Vi 2 sin 2  g a) H = b) H = 2 2 Vi cos  2g

D B earth.C

A

4.

c) H = Vi 2 sin  g

Vi 2 sin 2  2g

d)

H=

D

A C A b)

D

B C B

14.

The horizontal range of a projectile can be found by the formula: Vi 2 sin 2  Vi 2 cos 2  2g 2g a) R = b) R = Vi 2 cos 2  g

2

Vi sin 2θ g d) R =

c) R = 15. For a given value of initial velocity, the maximum range of a projectile can be achieved by throwing it at an angle of: a) 90o b) 60o o c) 45 d) 30o 16. For a given value of Vi, the maximum range of a projectile is given by: Vi 2 2Vi 2 2g g a) Rmax = b) Rmax = Vi 2 2Vi g c) Rmax = d) Rmax = 2 17. For any value of initial velocity, the minimum range of projectile is obtained by throwing it at an angle of: a) 90o or 0o b) 30o or 60o o o c) 40 or 50 d) 45o 18. The total time taken by a projectile from starting at the surface of the earth to landing again on it is given by: 2Vi sin  Vi sin  g g a) T = b) T = Vi sin  Vi cos  2g 2g c) T = d) T = 19. The position vector of a projectile is described by: 1  1    g 2 V V 2 i r r a) = t+ t b) = t - 2 g t2    c) r = V i t + gt2 d) r = V i t - g t2 20. Circular motion is an example of motion in: a) One dimension b) Two dimensions c) Three dimensions d) No dimension 21. In a circular motion, the acceleration is always directed towards: a) The centre b) The tangent c) Between the tangent and the normal d) None of the above 22. For a vehicle moving on a curved path the centripetal acceleration is provided by the: a) Air pressure b) Engine c) Shape of the wheels d) Force of friction 23. It is more convenient to measure the angular displacement in: a) Degrees b) Radians c) Grades d) Arcs 24. The number of radians in a complete circle is: a) 360 b) 180 c)  d) 2  25. If  is measured in radians, the length of arc S can be found by the relation: r   a) S = b) S = r c) S = r  d) S = r2  26. Angular displacement is the _______ that a body traces while moving in a circle: a) Length of arc b) Distance from a fixed point c) Angle d) None of the above 27. The magnitude of the angular velocity is given by:     a) =r b) = t

28.

D

2 r2 c)  = t d)  =  The time period is defined as the time required to traverse _______ by a revolving body:

C

C

A B

A

B A D B D C

C B

C

29.

a) One radian b) 180 degrees c) One revolution d) 90 degrees The relation between time period and angular velocity is: 2 a)  = 2  T b)  = T

B

30.

T 2T 2    c) = d) =  The magnitude of the linear velocity of a revolving body is given by: r   a) V = r b) V =

A

 c) V = r 31.

The direction of angular velocity a) Parallel to it c) At an angle of 180o

2 d) V = r

  with respect to position vector r is: b) Perpendicular to it d) At an angle of 270o

  32. The relation between the angular velocity  , the linear velocity V and the position vector r of a body is:     a) V = r   b) V =   r     c)  = V  r d) r = V   33. The instantaneous angular acceleration is given by the formula: dV  a)  = dt

34.

35.

36.

37. 38.

39.

40. 41.

42.

revolving

B

D

dr  b)  = dt

d d   c)  = dt d)  = dt The relationship between angular acceleration and linear acceleration is:       a)  = a   b)  =   a       c) a =    d)  = a   The value of centripetal acceleration can be found by the formula: V2 a) a = V2r b) a = r r V 2 c) a = r d) a = V The magnitude of the centripetal force can be obtained by the relation: a) Fc = mV2r b) Fc = mVr mV 2 1 mV 2 c) Fc = r d) Fc = 2 r To keep the planets revolving around the sun the centripetal force is provided by: a) The gravitational pull b) Inertia of the planets c) Momentum d) Some unknown force The dimensions of angular acceleration are: 2 2 a) T b) LT

  LT 

B





1 c) d)  LT   The relation between the moment of inertia I, torque and angular acceleration  is given by: a)  = I2  b) I =     c) =I d)  =  I Motion along a straight line is called motion in _______. a) One dimension b) Second dimension c) Fourth dimension d) None of these When a body moves in a plane, its motion in a plane is called motion in _______. a) One dimension b) Two dimension c) Uniform speed d) None of these

Let “ V i” be the initial velocity of any body then, we can write it in the following components as:

C

B

C

A A

C

A B A

ˆ ˆ ˆ ˆ a) V i = Vix i + Viy j b) V i = Vix i - Viy j ˆ ˆ ˆ ˆ c) V f = Viy i + Viy j d) V f = Vix i + Viy j 43. When the body is thrown upward making an angle of “  ” with the horizontal and moves freely action of gravity, it is called a _______. a) Horizontal b) Vertical c) Projectile d) None of these 44. The trajectory of a projectile is usually a _______. a) Trajectory b) Parabola c) Velocity d) Acceleration 45. The parabolic motion of a body is called _______. a) Projectile motion b) Tragectory motion c) Vertical motion d) None of these 46. In projectile motion, the value of acceleration along x-axis is _______. a) ax = 0 b) ax = 10 c) ax = 4 d) ax = 40 47. In projectile motion, the value of acceleration along y-axis is _______. a) ay = g b) ay = -g c) ay = -a d) None of these 48. In projectile motion, the value of displacement along x-axis is _______. a) x = vi cos  t b) x = vi sin  t c) Y = Vi cos  t d) Y = Vi cos  t 49. In projectile motion, the value of displacement along Y-axis is ________. 1 a) X = vi cos  t b) Y = vi sin  t - 2 gt2 1  c) Y = vi sin + 2 gt2 d) None of these 50. The velocity of a projectile at any instant (t) is given by _______. a) V = V x + V y

under

theC

B A A B A

B

A

b) V = V x - V y

c) V f = V x + V y d) V i = V x + V y 51. For maximum horizontal range, the formula is: D 2 2 Vi  Vi g g a) R (max) = b) R (max) = 2Vi 2 g c) R (max) = d) None of these 52. The position of the projectile at any instant (t) is given as _______. A   ˆ ˆ ˆ ˆ a) r = x i + y j b) r = x i - y j   ˆ ˆ ˆ ˆ c) r = x j + y i d) r = x j - y i 53. For a given value of _______ the maximum range of a projectile can be achieved by throwing it at an B angle of 45o: a) Acceleration b) Initial velocity c) Average acceleration d) None of these A mv 2 54. The work done in moving a body of mass m by the centripetal force r over half the circumference of the circle of radius r with speed V is: v2 a) Zero b) r

55.

56.

r 2 mv 2 2 r c) d) mv The unit of angular displacement is _______. a) Nm b) Degree or radian c) N/Kg d) Kgm/s  The relation between arc “s” and “ ” (measured in radians) is _______. a) 4S = r  b) r = S 

B C

57. 58. 59.

60.

61.

62.

r   c) S = r d) S = The relation between degree and radian is _______. a) 1 rad = 57.3o b) 1 rad = 117.5o o c) 1 rad = 73.5 d) 1 rad = 216.7o The rate of change of angular displacement is known as _______. a) Acceleration b) Angular velocity c) Angular acceleration d) None of these The formula for angular velocity is _______.  2   t w w a) = b) = t     c) w = 2 t d) w = 3t The formula for instantaneous angular velocity is _______. Lim Lim    t t  t  0  t  1 a) Winst = b) Winst = Lim  c) Winst = t  10 t d) None of these The relation between linear and angular velocity is defined by the relation _______. a) V = r  b) V = rw2 3 c) V = r  d) V2 = r  The formula for angular acceleration is _______.  a) V = r  b)  = t

  c) =  d) None of these 63. The force which is needed to move a body in a circular path and which is always directed towards the is called _______. a) Centripetal force b) Centripetal acceleration c) Hyperbola d) None of these 64. The relationship between angular acceleration and linear acceleration is _______.       a)  = a   b) a =       c)  = a   d) None of these 65. The formula for instantaneous angular acceleration is _______.   dw dw  a)  = dt b) V = dt  dw  a c) = dt d) None of these 66. The formula for centripetal acceleration is _______. V2 V3 a) a = r b) a = r

67. follow: 68. 69. 70.

A B A

A

A

B

center,A

B

A

A

V2 V 2 r c) a = d) a = r An object thrown in arbitrary direction, in space with an initial velocity and moving freely under gravity willD a) A circle b) A straight line c) A hyperbola d) A parabola The vertical component of velocity of projectile, during its motion, is minimum: a) At the time of projection b) At the highest point of its trajectory c) Just before hitting the plane of projection d) None of the above The horizontal range of a projectile, at a certain place, depends upon: a) The mass of the projectile b) The velocity of projection c) The angle of projection d) The angle as well as velocity of projection The projectile attains maximum horizontal range when it is projected at an angle of: a) 30o with the horizontal b) 45o with the horizontal o c) 60 with the horizontal d) 90o with the horizontal

B D B

71.

The velocity of a projectile is maximum: C a) At half of the height b) At one-fourth of the height c) Just before striking the ground and point of projection d) None of the above 72. The angle subtended at the centre by a body moving along a circle is called: C a) Angular speed b) Angular velocity c) Angular displacement d) Angular acceleration 73. The angle subtended at the centre of a circle by an arc of length equal to its radius is equal to: D a) One rotation b) Half rotation c) One degree d) One radian 74. The force responsible for the circular motion of the electron around the nucleus is: C a) Gravitational force b) Frictional force c) Coulomb force d) Cohesive force 75. The time rate of change of angular displacement is called: A a) Angular velocity b) Angular acceleration c) Angular displacement d) Angular speed 76. The direction of linear velocity of a body at a point moving along a circular path is: A a) Along the tangent b) Along the axis of rotation c) Directed away from the centre d) Directed towards the centre C 77. When a body moves in a circle, the angle between its linear velocity  and angular velocity  is: a) 0o b) 45o c) 90o d) 180o 78. When an object moves with uniform speed in a circular orbit, its centripetal acceleration must be directed: B a) Along the direction of motion b) Towards the centre of circle c) Perpendicular to the centre of circle d) Away from the centre of circle 79. A satellite remains in an orbit around the earth due to the centripetal force provided by: B a) Gravitational pull of the sun on the satellite b) Gravitational pull of the earth on the satellite c) The rocket engine attached to the satellite d) None of the above 80. At which place the motion of a pendulum becomes fastest? D a) K-2 b) Muree c) Lahore d) Karachi 81. When an object moves along a circular path its velocity: B a) Remains constant b) Changes continuously c) Becomes zero d) None of the above 82. A mass m is suspended from a string attached to the ceiling of an elevator. The elevator has acceleration D “a” upward. The tension in the string is: a) m a b) m g c) m g – m a d) m g + ma 83. When a stone is whirled in a horizontal circle by means of a string, the centripetal force is supplied by: C a) Velocity of the stone b) Mass of the stone c) Tension in the string d) Air friction 84. When a stone is whirled in a vertical circle at the end of a string, the tension in the string is maximum: D a) At the centre b) At the top c) At the horizontal diameter d) At the bottom 85. The acceleration of a body undergoing uniform circular motion is constant in: B a) Direction only b) Magnitude only c) Both magnitude and direction d) Neither magnitude nor direction 86. A stone is whirled in a vertical circle at the end of a string. When the stone is at the highest position, the A tension in the string is: a) Zero b) Maximum c) Greater than the weight of the stone d) Equal to the weight of the stone 87. A car moves with a uniform speed of 2 m/s in a circle of radius 0.4 m. Its angular speed in rad/sec is: D a) 0.8 b) 1.6 c) 4 d) 5 88. A ball is thrown horizontally from the top of a cliff with a speed of 40 m/s. It hits the ground in 2 seconds. C What is the distance from the cliff to the point at which the ball hits the ground. a) 20 m b) 40 m c) 80 m d) 19.6 m 89. A body of mass m moves in a circle of radius r with constant angular velocity  about a point. What is C Its angular momentum about this point? a) m  b) mr  90.

2 c) mr2  d) mr  If a body of mass m is moving with constant speed V (also called tangential velocity) in a circular path

ofC

radius r, its tangential acceleration is: a) r V2 b) V2/r c) Zero d) None of these 91. A body of mass m moves at constant angular speed  in a horizontal circle of radius r. What is the work on the body in one revolution? 2 a) Zero b) 2  mr2 

doneA

2 2 c)  mr3  d) mr2  92. Which of the following statements is correct for a particle moving in a horizontal circle with constant B angular velocity? a) The linear momentum is constant but the kinetic energy varies b) The kinetic energy is constant but the linear momentum varies c) Both kinetic energy and linear momentum are constant d) Neither the linear momentum nor the kinetic energy is constant 93. A point on the rim of a wheel moves 0.2 m when the wheel turns through an angle of 0.1 rad. What is B the radius of the wheel? a) 0.5 m b) 2 m c) 0.2 m d) 20 m 94. A car of mass 1 kg moves round a curve whose radius of curvature is 100 m at a speed of 10 ms-1. What is theB centripetal force on the car? a) 10 N b) 1 N c) 100 N d) 0.1 N 95. A body in simple harmonic motion makes n complete oscillations in one second. Its frequency is: C a) 1 hertz b) 1/n hertz c) n hertz d) Zero 96. A ball is thrown horizontally from the top of a cliff with a velocity of 10 ms-1. The ball takes 4 seconds toA reach the ground. The horizontal distance traveled by the ball is: a) 40 m b) 2.5 m c) 0.4 m d) 78.4 m 97. A projectile is thrown with a speed of 100 ms -1 in a direction 60o with the horizontal. The horizontal B component of its velocity is: a) 86.6 ms-1 b) 50 ms-1 -1 c) 60 ms d) 163.2 ms-1 98. The centripetal acceleration of a body moving with velocity 2 ms-1 in a circle of radius 0.3 m is: B a) 0.6 ms-2 b) 13.3 ms-2 c) 0.15 ms-2 d) 6.6 ms-2 99. A vehicle of mass 20 Kg moves round a curve whose radius of curvature is 10m at a speed of 20ms -1 A The centripetal force on the vehicle is: a) 800 N b) 200 N c) 4000 N d) 40 N 100. The angular speed of second’s hand of a watch in rad/s is: C   a) 3 b) 6

101. 102. 103.

104. 105.

 30 c) d) Motion of projectile is: a) One dimensional b) c) Three dimensional d) The angular velocity at any instant is called: a) The instantaneous displacement b) c) The instantaneous angular velocity In circular motion average angular velocity is given by:

 a)  av = t t c)  av = 

 12 B Two dimensional Four dimensional C Average angular velocity d) The instantaneous speed A

 av =   t  d)  av = 2 t b)

The angle subtended at the center of a circle by an arc equal to its radius is equal to: a) One radian b) One rotation c) One degree d) Half rotation Centripetal force is given by:

A B

a)

106.

107.

108.

m2v r

b)

mv 2 r

2

m v

mv 2

2

r2

c) r d) Average angular velocity is mathematically defined as: a) V/2 i  f 2 c) The circumference of the circle is equal to: a) 2  r c)  r Period of circular motion is given by: 2 a) T = 

b) d)

V0  V 2 V0   i 2

b) 2  r2 2 d)  r

C

A

C  b) T =  

2 2 c) T =  d) T =  109. Equation for motion in a straight line is: D a) V = U + at b) S = Ut + 1/2 at2 c) V2 = U2 + 2aS d) All of the above 110. The horizontal range of a projectile is bigger when it is thrown at an angle of: D a) 60o b) 90o c) 180o d) 360o 111. Centripetal force performs: D a) Maximum work b) Negative work c) Minimum work d) No work 112. A body is moving with a constant speed v in a circle of radius r. Its angular acceleration is: C a) vr b) v/r c) Zero d) vr2 113. If a particle moves in a circle describing equal angles in equal interval of times, Its velocity vector: C a) Remains constant b) Changes in magnitude c) Changes in direction d) Changes both in magnitude and direction 114. ON a railway curve the outside rail is laid higher than the inside on so that resultant force exerted on the C wheels of the rail car by the tops of the rail will: a) Have a horizontal inward component b) Be vertical c) Equilibrate the centripetal force d) Be decreased 115. A cyclist turns around a curve at 15 miles/hour. If he turns at double the speed, the tendency to over B turn is: a) Doubled b) Quadrupled c) Halved d) Unchanged 116. A car moving on a horizontal road may be thrown out of the road taking a turn: B a) By the gravitational force b) Due to the lack of proper centripetal force c) Due to the rolling frictional force between the tire and road d) Due to the reaction of the ground 117. An airplane is taking a turn in a horizontal plane. While doing so it: B a) Remains horizontal b) Inclines inwards c) Inclines outwards d) Makes wings vertical 118. A car sometimes overturns while taking a turn. When it overturns, it is: A a) The inner wheel which leaves the ground first b) The outer wheel which leaves the ground first c) both the wheels leave the ground simultaneously d) either wheel which leaves the ground first 119. Which of the following statements is correct? The rotational energy of a body for a given angular speed D depends on its: a) Mass only b) Size only c) Mass and size d) Mass as well as distribution of mass about the axis of rotation 120. The mud flies off the tyre of a moving bicycle in the direction of: C a) Towards the centre b) Radius c) Tangent to the tyre d) Motion

121. 122. 123. then his: 124. 125.

126. 127.

128. 129.

130. is:

131. 132. 133. 134. 135. 136.

The ratio of angular speeds of minutes hand and hour hand of a watch is: C a) 1:2 b) 6:1 c) 12:1 d) 1:6 When a mass is rotating in a plane about a fixed point, its angular momentum its directed along: C a) The radius b) Tangent to the orbit c) line perpendicular to the plane of rotation d) None of these A man is sitting on a rotating table with his arms stretched outwards. When he suddenly folds his arms insideC a) Angular velocity will decrease b) Angular velocity remains constant c) Moment of inertia decreases d) Angular momentum increases An example of projectile motion is: D a) A bullet shot from a rifle b) An object dropped from an airplane c) A thrown football d) All of the above Relation between linear velocity of a rotating body and its angular velocity is: A a) V =   r b) V =  . R c) V = r   d) V =  + r A body can have constant velocity when it follows a: B a) Circular path b) Rectilinear path c) Elliptical path d) Zig-Zag path What is the outward force acting on a mass of 10 Kg tied to one end of an inelastic string 10m long A and rotated at a speed of 1m/s? a) 1 N b) 2 N c) 2.5 N d) 10 N To improve the jumping record, a long jumper should: B a) Jump as high as possible b) Jump at an angle of 45o c) Jump at an angle of 60o d) None of the above The shaft of a motor rotates at a constant angular speed of 3600 revolution per minute. Angle turned B through in 1 sec in radians is: a)  b) 2   c) 6 d) 120  When a wheel 1m in diameter, makes 30 revolutions per minute, the linear speed of a point on its rim in m/secB a)  b)  /2  c) 130 d) 60  The dimensional formula for angular velocity will be: a) M0 L0 T-1 b) M0 L0 T-2 -1 0 c) M L T d) M L T-3 A bomber drops its bombs when it is vertically above the target. It misses the target due to: a) The horizontal component of velocity b) The vertical component of the velocity c) Pull of gravity d) Air resistance One radian is equal to: a) 67.3o b) 57.3o o c) 87.3 d) 60o The angular displacement per second (per unit time) is called: a) Angular acceleration b) Angular rotation c) Angular velocity d) Angular speed The unit of angular velocity in SI unit is: a) Radian s-1 b) Meter s-1 -1 c) Degree s d) Revolution s-1 The unit of angular acceleration in SI units is: a) Radian s-1 b) Radian-2 s-1 -2 c) Radian s d) Radian

A A B C A C