unit 3 final.pdf

Gaurav Burhade’s Structure Academy |Contact No.: 8551988111 1
Gaurav Burhade’s
STRUCTURE ACADEMY
A. CURVILINEAR MOTION
1. If sx = t2
+ t + 4 m and sy = 4t m then at t = 3 s, the magnitude of displacement is
A) 4 m B) 5 m C) 20 m D) 10 m
2. If ax = t2
+ t + 4 m/s2
and ay = 8t m/s2
then at t = 1 s, the angle θ made by acceleration
with x-axis is
A) tan-1
4/3 B) tan-1
5/4 C) tan-1
5/3 D) None of these
3. Radius of curvature for a particle moving along a curve y = f(x), is given by
A) [1+(dy/dx)2
]3/2
/(d2
y/dx2
)
B) [1-(dy/dx)2
]3/2
/(d2
y/dx2
)
C) [1+(dy/dx)3/2
]2
/(d2
y/dx2
)
D) [1+(dy/dx)2
]3/2
/(dy/dx)
4. In curvilinear motion, acceleration of a particle is always
A) Normal to path of particle
B) Tangential to path of particle
C) Along the direction of velocity
D) Never tangential to the path of particle.
5. If vx = t2
+ t + 4 m/s and vy = 4t m/s then at t = 1 s, the magnitude of acceleration is
A) 4 m/s2
B) 5 m/s 2
C) 20 m /s2
D) 10 m/s2
6. If sx = t2
+ t + 4 m and sy = 4t m then at t = 1 s, the angle θ made by velocity with x-axis
is
A) tan-1
4/3 B) tan-1
5/4 C) tan-1
7. If vx = t2
+ t + 4 m/s and vy = 4t m/s then at t = 1 s, the angle θ made by acceleration with
x-axis is
A) tan-1
4/3 B) tan-1
5/4 C) tan-1
8. A rotor 25mm in diameter is spinning at 200 rps. Find normal component of acceleration
of a point on rim.
A) 20000 m/s2
B) 19800 m/s2
C) 19739 m/s2

D) 19500 m/s2
9. Motion of a particle is defined by x = 4 + 3t2
and y = 3 + t3
, acceleration of particle at t =
0 is
A) 5 m/s2
B) 3 m/s2
C) 4 m/s2
D) 6 m/s2
10. A train starting from rest is moving along curved track with constant acceleration and
attains a speed of 60 kmph in 3 minutes. Determine acceleration of the train 1 minute
after leaving the station. The radius of curvature of the track is 800 m.
A) 0.1 m/s2
B) 0.11 m/s2
C) 0.22 m/s2
D) 0.2 m/s2
11. A rocket moves along a curved path with linear velocity of 600 m/s and it is observed
that the rocket experiences an acceleration of 10 g in a direction normal to the path. Find
the radius of curved path
A) 6377 m B) 7746 m C) 3669.7 m D) 3333 m
12. A train enters a curve of radius 100 m with a velocity of 20 m/s and accelerates uniformly
to 30 m/s over a distance of 200 m. Determine the acceleration when the train has
covered a distance of 100 m from the start of the curve.
A) 9.62 m/s2
B) 6.62 m/s2
C) 1.42 m/s2
D) 12.72 m/s2
13. In path coordinate, frictional force always acts along
A) Normal direction
B) Tangential direction
C) a and b
D) None of above
14. ∑Fn = man, equation of motion along
A) Tangential direction
B) Radial direction
C) Transverse direction
D) Normal direction
15. Equation of motion in normal direction is written as ∑Fn = man, where ∑Fn is referred to as
the ------
A) Impulse
B) Normal force
C) Tangential force
D) Inertial force
16. Equation of motion in normal direction is written as ∑Fn = man, where an is referred as
A) Tangential component of acceleration
B) Transverse component of acceleration
C) Total acceleration
D) Normal component of acceleration

17. When a car moves over a trough, the pressure exerted by the wheels on the road is
A) Same as that on the level road
B) Greater than that on the level road
C) Less than that on the level road
D) Zero
18. When a stone tied to one end of a string is whirled in a verticle circle, the tension in a
string is maximum at
A) The lowest point
B) The highest point
C) The mid point
D) 45 degree to verticle
19. When a stone tied to one end of a string is whirled in a verticle circle, the tension in a
string is minimum at
A) The lowest point
B) The highest point
C) The mid point
D) 45 degree to verticle
20. ∑Ft = mdv/dt, equation of motion along
A) Normal direction
C) Both a and b
D) None of these
21. ∑Fn = mv2
/ρ, equation of motion along
A) Normal direction
C) Both a and b
D) None of these
22. If dr/dt is zero for a particle, the particle is
A) Not moving
B) Moving in circular path
C) Moving in a straight line
D) Moving with constant velocity
23. If the pendulum is released from rest in its unstable vertical equilibrium position, determine
the magnitude of force in the rod at which the axial force in the rod changes from
compression to tension.
A) More than weight of pendulum
B) Less than weight of pendulum
C) Zero
D) None of these

24. A small vehicle travel on the top of circular path in a vertical plane. Determine the magnitude
of normal reaction at which the vechicle leave the circular path
A) Less than weight of vehicle
B) More than weight of vehicle
C) Zero
D) None of these
25. In merry go round, the chairs are supported by cables, If the angular speed of merry go round
increases then chairs swings
A) Towards axis of rotation
B) Away from axis of rotation
C) Cable makes same angle with vertical
D) None of these
26. In merry go round, the chairs are supported by cables, If the angular speed of merry go
round decreases then chairs swings
A) Towards axis of rotation
B) Away from axis of rotation
C) Cable makes same angle with vertical
D) None of these
27. For a redundant truss the number of members ‘n’ are,
A) Less than (2j- 3)
B) Equal to (2j- 3)
C) More than (2j- 3)
D) none of these
28. In projectile motion, at the highest point the direction of velocity is
A) Upwards
B) Downward
C) Tangential to path
D) Normal to path
29. Newton’s second law can be written as mathematically, ∑ Fn = man, within the
summation of forces ∑F------ are (is) included.
A) External forces
B) Weight
C) Internal force
D) All of above
30. When a car of mass m moves with velocity v over a trough of radius of curvature ρ , the
normal reaction exerted by the wheels on the road is
A) N = mv2
/ρ - mg
B) N = mv2
/ρ + mg
C) N = mv2
+ mg
D) None of these

31. In polar system 2(dr/dt) x (dθ/dt) is called
A) Coriolis acceleration
B) Radial acceleration
C) Transverse acceleration
D) None of above
32. If acceleration of particle is zero, it implies
A) Velocity of particle is constant
B) Velocity of particle is zero
C) Radius of curvature is zero
D) Velocity of particle is constant and travels along a straight path
33. Hodograph is the curve
A) Joining the ends of velocity vectors drawn from a common point
B) Joining acceleration vectors
C) Joining the velocity vector tail to head
D) None of above
34. Acceleration of a particle is tangential to
A) Path of a particle
B) Hodograph
C) Radial direction
D) Normal direction
35. In curvilinear motion normal component of acceleration represents
A) Rate of change of magnitude of velocity
B) Rate of change of direction of velocity
C) Both a and b
D) None of the above
36. Magnitude of the normal component of acceleration is
A) Directly proportional to radius of curvature
B) Inversely proportional to radius of curvature
C) Negative
D) Zero at constant velocity
37. The direction of the tangential component of acceleration and velocity are always
A) Perpendicular to each other
B) In opposite direction
C) Collinear
D) In same direction
38. In polar coordinate system the term dθ/dt is called
A) Angular velocity
B) Transverse component of velocity

C) Radial component of velocity
D) Tangential component of velocity
39. When a car moves over a hump, the pressure exerted by the wheels on the road is
A) Same as that on the level road
B) Greater than that on the level road
C) Less than that on the level road
D) Zero
40. In polar coordinate system dr/dt is called
A) Angular velocity
41. In polar coordinate system rdθ/dt is called
A) Angular velocity
42. In polar coordinate system d2
r/dt2
is called
A) Radial component of acceleration
C) Angular acceleration
θ/dt2
is called
r/dt2
+ 2(dr/dt)(dθ/dt) is called
45. A particle is traversing a curved path with a speed of 90 kmph. If the normal component
of acceleration is 1 m/s2
. Determine the radius of curvature
A) 200 m B) 625 m C) 300 m D) 825 m

46. A particle is traversing a curved path with a speed of 72 kmph. If the normal component
of acceleration is 2.5 m/s2
. Determine the radius of curvature.
A) 200 m B) 260 m C) 160 m D) 525 m
47. A motorcyclist in a circus rides his motorcycle within the confines of the hollow sphere.
If the coefficient of static friction is 0.4, determine the frictional force at which he must
travel if he is to ride along the wall when θ = 90 degree. The mass of motor cycle with
rider is 250 kg.
A) 2452.5 N B) 981 N C) 6131.25 N D) None of these
48. A rotor 30mm in diameter is spinning at 300 rps. Find normal component of acceleration
of a point on rim.
A) 53295.8 m/s2
B) 19800 m/s2
C) 19700 m/s2
D) 19500 m/s2
49. If the pendulum is released from rest in its unstable vertical equilibrium position,
determine the nature of force in the rod at which the axial force in the rod changes from
compression to tension.
A) Compressive B) Tensile C) Null D) None of these
50. A motorcyclist in a circus rides his motorcycle within the confines of the hollow sphere.
If the coefficient of static friction is 0.4, determine the Normal reaction at which he must
travel if he is to ride along the wall when θ = 90 degree. The mass of motor cycle with
rider is 250 kg.
A) 2452.5 N B) 981 N C) 6131.25 N D) None of these
51. A train enters a curved horizontal track at a speed of 72 kmph and accelerates uniformly
to 108 kmph in 12 s. Calculate tangential component of acceleration.
A) (- 0.5) m/s2
B) (+ 0.5) m/s2
C) (- 0.833) m/s2
D) (+ 0.833) m/s2
52. Find the couple applied on fly wheel if tension in tight side 200N, tension is slack side
100N & R = 0.4m
A) 40 Nm B) 120 Nm C) 20 Nm D) None of the above
53. A particle moving with constant velocity along the circular path in a horizontal plane, the
equation of kinetis is not applicable to solve the problem
A) ΣFn = m an B) ΣFt = m at C) Both a and b D) None of these
54. The equation of motion, in kinetics of curvilinear motion of particle are
A) ΣFn = m an
B) ΣFt = m at C) ΣFb = 0 D) All of these
55. The pendulum bob has a mass 10 kg and is released from rest when θ = 0 with horizontal.
If the length of cord is 1 m, determine the velocity of the bob at θ = 30 degree.
A) 9.81 m/s B) 3.13 m/s C) 3.84 m/s D) None of these

56. During the journey, a 250 kg car traveling at speed of 9.81 m/s just loose the contact with
the road as it reaches the crest of the hill, determine the radius of curvature.
A) 1 m B) 9.81 m C) 4.905 m D) None of these
57. The driver of a car traveling along a straight level road suddenly apply a breaks so that
the car moved with constant deceleration of 2.453 m/s2
. Find the coefficient friction
between the tyres and road.
A) 0.25 B) 0.5 C) 0.75 D) None of these
58. A particle moves along a path r = (8t2
)i + (t3
+ 5)j, magnitude of particles velocity at
t = 3 s is
A) 55.07 m/s B) 5.507 m/s C) 50.5 m/s D) 24.1 m/s
59. A 600 kg wreeking ball is attached to a cable of length 12 m and negligible mass. The
velocity of the ball is 8 m/s when the cable is vertical. Determine the tension in the cable
if the ball swing in the vertical plane.
A) 9810 N B) 9806 N C) 2686 N D) None of these
60. The pendulum bob has a mass m and is released from rest when θ = 0 with horizontal. If
the length of cord is l, then the velocity of the bob as a function of angle of descent θ is
given by
A) v2
= 2gl sin θ B) v2
= 3gl sin θ C) v2
= 4gl sin θ D) v2
= 2gl cos θ
61. The pendulum bob has a mass 10 kg and is released from rest when θ = 0 with horizontal.
Determine the tension in the cord at θ = 30 degree.
A) 147.15 N B) 98.1 N C) 254.87 N D) None of these
62. A girl having mass of 25 kg sits on the merry go round at a distance of 1.5 m from the
centre of rotation. Determine the maximum constant speed at which she slip off the merry
go round if the coefficient of static friction is 0.3.
63. The man has a mass of 80 kg and sits at 3 m from the centre of the rotating platform.
Determine the maximum velocity at which he can slip from the rotating platform if the
coefficient of static friction between contact surface is 0.3.
64. The man has a mass of 80 kg and sits at r from the centre of the rotating platform. The
maximum velocity at which he can slip from the rotating platform is 2.97 m/s and the
coefficient of static friction between contact surface is 0.3. Determine the distance r.
A) 9.8 m B) 2.94 m C) 0.9 m D) 3 m

65. A particle moving with constant velocity along the circular path in a horizontal plane, the
equation of kinetis is not applicable to solve the problem
A) ΣFn = m .an B) ΣFt = m. at C) Both a and b D) None of these
66. The driver of a car traveling along a straight level road suddenly apply a breaks so that
the car moved with constant deceleration of 4.905 m/s2
. Find the coefficient friction
between the tyres and road.
67. The girl of mass m is in the lowest position in a swing in a vertical plane. The effective
length from mass centre to the fixed support for the rope is 10 m and the velocity of the
girl mass centre is 10 m/s, determine the mass of girl if tension in the rope is 990.5 N.
A) 50 kg B) 40 kg C) 60 kg D) None of these
68. The equation of motion, in kinetics of curvilinear motion of particle are
A) ΣFn = m an B) ΣFt = m at C) ΣFz = 0 D) All of these
69. A bob of 1 m pendulum describe an arc of a circle in a vertical plane. When the angle of
the cord is 300
with the vertical, the tension in the cord is 95 N. Find the mass of
pendulum if its velocity at this instant is 1 m/s.
A) 5 kg B) 100 kg C) 10 kg D) None of these
70. A 60 kg wreeking ball is attached to 15 m long steel cable and swing in a vertical arc.
Determine the velocity of the ball at the bottom if the tension in the cable is 690 N.
71. A particle is moving in x-y plane with y component of velocity, vy = 6t m/s, where t is in
seconds. If ax = 3t m/s2
, when t = 0, x = 3m, y = 0 and vx = 0. What is value of x when t = 2s.
A) 123 m B) 34 m C) 23 m D) 67.08 m
72. Motion of particle is defined by x = 1- t and y = t2
, what is the equation of path
A) y = (x -1)2
B) y = (1- x)2
C) y = (x + 1)2
D) y = (x -1)2/3
73. Motion of particles A and B is described by the position vectors rA = 3ti + 9t(2 - t)j and rB
= 3(t2
- 2t + 2)i + 3(t - 2)j. time at which the two particles collide is
A) 2 s B) 4.5 s C) 3 s D) 9 s
74. In case of tracking of space vehicles ------ system of coordinates is useful
A) Cartesian B) polar C) path D) All
75. At the point on the curve, the normal acceleration a n = 0 because at that point radius of
curvature becomes --------
A) Zero B) One C) Infinite D) None of these

76. A girl having mass of 50 kg sits on the merry go round at a distance of 1.5 m from the
centre of rotation. Determine the coefficient of static friction if maximum constant speed
is 3 m/s at which she slip off the merry go round.
77. If a particle moving in a circular path of radius 5 m and a velocity is expressed as v = 4t2
m/s. What is the magnitude of its total acceleration at t =1s?
A) 8 m/s2
B) 8.62 m/s2
C) 3.2 m/s2
D) 11.2 m/s2
78. A beam AB of span 1 m, hinged at ‘A’ and simply supported at ‘B’ is loaded with u.v.l.
of 10 N/m intensity at end ‘A’ and 20 N/m at end ‘B’. The reaction at end ‘A’ are –
A) 6.66 N (upwards)
B) 8.33 N (upwards)
C) 10 N (upwards)
D) 20 N (upwards)
79. A man standing at the rear end of an open truck moving with uniform acceleration throws
a ball vertically upwards. The ball will fall
A) Behind the truck
B) Ahead of truck
C) Into his hands
D) On to the truck but not in his hands
80. The 50 kg girl is in the lowest position in a swing in a vertical plane. The effective length
from mass centre to the fixed support for the rope is 10 m. Determine the velocity of the
girl mass centre if tension in the rope is 990.5 N.
A) 100 m/s B) 17.21 m/s C) 10 m/s D) None of these
81. If a particle is moving in a circular path with constant velocity , its radial acceleration is
A) Zero B) -r(d2
θ/dt2
) C) d2
r/dt2
D) (dθ/dt) x (dr/dt)
82. The radial component of acceleration of particle moving in a curvilinear path is always
A) Negative
B) Perpendicular to the transverse component of acceleration
C) directed towards centre of path
D) All above
83. If motion of particle is expressed as x = t2
+ 4 and y = t2
- 4 then the velocity at t = 2 s, is
A) 4 m/s B) 5 m/s C) 4√2 m /s D) 10 m/s.
84. The radial component of velocity of a particle moving in a circular path is always
A) Zero
B) Greater than its transverse components
C) Constant
D) Less than its transverse components

85. Normal component of acceleration is zero if
A) Path is circular
B) Velocity is constant
C) Path is rectilinear
D) None of above
86. Positive normal direction in case of path coordinate system is
A) Normal to tangential component
B) Always directed towards the centre of curvature
C) Normal to bi-normal component
D) All of above
87. When particle travels along a circular path, then radius of curvature is
A) Diameter of circle
B) Circumference of circle
C) Area of circle
D) Radius of circle
88. An airplane making a turn at constant speed is experiencing
A) Tangential acceleration
B) Normal acceleration
C) Both acceleration
D) No acceleration
89. Space shuttle goes from rest to 348 m/s in first 12 s of its launch, it’s average acceleration is
A) 2.4 m/s2
B) 174 m/s2
C) 29 m/s2
D) 4176 m/s2
90. The direction of normal component of acceleration for a particle on curved path is
A) Always directed towards the centre of curvature
B) Always away from centre of curvature
C) Depends on the problem
D) None of these
91. ∑Ft = mvdv/ρds, equation of motion along
A) Normal direction
C) Both a and b
D) None of these
92. Tangential component of acceleration for a particle on curved path reflects
A) Speed of the particle
B) Direction of motion of particle

C) Change in direction of particle
D) Change in speed of particle
93. Normal component of acceleration for a particle on curved path represents
A) Speed of the particle
B) Direction of motion of particle
C) Change in speed of particle
D) Change in direction of motion of particle
94. In curvilinear motion , velocity of a particle is always
C) Depends on acceleration
D) None of above
95. The magnitude of the normal component of acceleration is
A) Proportional to radius of curvature
B) Inversely proportional to radius of curvature.
C) Sometimes negative.
D) Zero when velocity is constant.
96. In curvilinear motion, acceleration of a particle is always
C) Depends on velocity of particle
D) Towards concave side of path of particle
97. A particle traveling along a curved path, the normal component of acceleration is equal to
A) v/ ρ B) v2
/ρ C) v x ρ D) v/ρ2
98. The motion of a particle is described by the following equations x = t2
+ 8t + 4, y = t3
+
3t2
+ 8t + 4, determine initial velocity of the particle.
A) 11.31 m/s B) 33.33 m/s C) 23.32 m/s D) 11.13 m/s
99. If vx = a sin ωt m/s and vy = a cos ωt m/s then at t = 3 s, the angle θ made by velocity
with y-axis is
A) Ω B) 2 ω C) 3 ω D) None of these
100. If sx = a sin ωt m and sy = a cos ωt m then at t = 3s, the angle θ made by velocity with x-
axis is
A) ω B) 2 ω C) 3 ω D) 180 - 3 ω

101. A missile is fired so as to reach maximum range then the maximum height reached is
A) Same as range
B) Three-forth of range
C) Half of range
D) One-forth of range
102. For a given velocity and horizontal range, the possible angle of projection
are
A) 1 B) 2 C) 3 D) 4
103. A ball is thrown horizontally with a velocity of 100 m/s from top of the building 300 m
high. The time taken by ball to reach ground is
A) 7.8 s B) 8.7 s C) 3 s D) 9 s
104. Co-ordinate of the projection of a ball are (0, 0) and the maximum height is (5 m, 5 m)
and the time to reach the maximum height is 5 s. Determine the initial velocity.
A) 25.25 m/s B) 26.26 m/s C) 30.30 m/s D) 22.22 m/s
105. A ball is projected at such an angle that the horizontal range is 4 times the maximum
height. Find the angle of projection.
A) 0 degree B) 30 degree C) 45 degree D) 90degree
106. A boy throws two stones in the sky one after another. He throws the first stone
vertically upward which takes t seconds to come back to the ground. He throws the
second stone with the same velocity as that of earlier but the angle of projection of 600
.
The time taken by the second stone to reach the ground shall be
A) Less than t
B) More than t
C) Same as t
107. A ball thrown at 450
with horizontal so as to clear fence 3 m high above the ground and
20 m away from the point. If the point of throw is 1 m above the ground find the initial
velocity of the throw.
A) 15.76 m/s B) 16.76 m/s C) 14.76 m/ s D) None of these
108. A projectile is fired with a velocity 75 m/s at an angle of 600
to the horizontal.
Determine the velocity of projectile after 0.5 s.
A) 80.00 m/s B) 70.79 m /s C) 79.10 m/s D) 22.22 m/s
109. For maximum horizontal range in a projectile motion the angle of projection is – degree
A) 90 B) 60 C) 45 D) 30
110. A ball is projected from an inclined plane at an angle of 300
with horizontal in the

downward direction with a velocity of 10 m/s perpendicular to the plane. If the ball
strikes the ground find the maximum range along the plane.
A) 13.59 m B) 59.13 m C) 13.95 m D) 95.13 m
111. An inclined plane has a rise of 5 in 12. A shot is projected with a velocity 250 m/s at an
elevation of 300
. Find the range of the plane if the shot is fired up the plane.
A) 6665 m B) 1555 m C) 1665 m D) 1228 m
112. The velocity of particle in projectile motion at top of its path is equal
to
A) Zero
B) Initial velocity of projection
C) Vertical component of initial velocity of projection
D) Horizontal component of initial velocity of projection.
113. In projectile motion acceleration along horizontal direction
is
A) Constant
B) Uniform
C) Zero
D) None of these
114. Motion of projectile along verticle direction is
under
A) Uniform acceleration
B) Constant acceleration
C) Gravitional acceleration
D) Variable acceleration
115. In projectile motion the velocity is always ----- .
A) Vertical
B) Horizontal
C) Tangential to path of particle
D) Normal to path of particle
116. In projectile motion, at the highest point the direction of velocity
is
E) Upwards
F) Downward
G) Tangential to path
H) Normal to path
117. If acceleration of particle is zero, it
implies
A) Velocity of particle is constant
B) Velocity of particle is zero

C) Radius of curvature is zero
D) Velocity of particle is constant and travels along a straight path
118. In projectile motion, the radius of curvature increases from
A) Point of maximum height to point of landing
B) Point of maximum height to point of projection
C) Point of projection to point of maximum height
D) a and b
119. A projectile is projected with an initial velocity of 40 m/s at an angle of 60 degree, the
horizontal component of velocity is
A) 20 m/s B) 34.64 m/s C) 25 m/s D) None of these
120. Determine the angle of projection when the missile projected with velocity of projectin
343.1 m/s and cover horizontal range of 12 km.
A) 30 degree B) 60 degree C) 45 degree D) 90 degree
121. In projectile motion, the radius of curvature at point of maximum height
is
A) Zero B) Minimum C) Maximum D) None of the above
122. In projectile motion, the magnitude of acceleration along x-axis is
A) (-9.81) m/s2
B) 9.81 m/s2
C) Zero D) None of these
123. Maximum range of projectile projected on horizontal ground is given by
A) u2
/2g B) u2
sin α /2g C) u2
/g D) u2
sin α /g
124. A particle moves along a path r = (8t2
)i + (t3
+ 5)j, magnitude of particles velocity
at t = 3 s is
B) 55.07 m/s B) 5.507 m/s C) 50.5 m/s D) 24.1 m/s
125. The horizontal range of projectile and maximum height reached by projectile is equal if
angle of projection is
A) tan-1
4 B) tan-1
¼ C) tan-1
2 D) 45
126. In projectile motion, the radius of curvature decreases from
A) Point of maximum height to point of landing
B) Point of maximum height to point of projection
C) Point of projection to point of maximum height
D) a and b
127. When a particle is projected from the top of a building strikes the ground away from the
building then its horizontal distance is

A) Same as range
B) Greater than range
C) Less than range
D) Zero
128. In projectile motion, the equation of trajectory
is
A) Linear
B) Parabolic
C) Cubic parabolic
D) None of these
129. In projectile motion, path followed by the particle is known
as
A) Flight
B) Trajectory
C) a and b
D) None of these
130. At the highest point of projectile motion, velocity and acceleration are ---
A) Parallel to each other
B) Inclined
C) Perpendicular to each other
D) None of above
131. A particle is projected horizontally at 36 m/s from a point 122.5 m above a horizontal surface ,
the time taken by the particle to reach the surface of ground is
A) 2 s B) 5 s C) 3 s D) 4.3 s
132. Space shuttle goes from rest to 348 m/s in first 12 s of its launch, it’s average acceleration is
B) 2.4 m/s2
B) 174 m/s2
C) 29 m/s2
D) 4176 m/s2
133. If two projectiles are fired with equal velocities but one with 30 0
and other with 60 0
with horizontal, then both will have
A) Same time of flight
B) Equal horizontal range
C) Equal horizontal range and same maximum height
D) Same maximum height
134. If the initial velocity is increased by 20% calculate the percentage increase in the
maximum range of projectile.
A) 10% B) 40% C) 50% D) 20%

135. The horizontal range of a projectile is maximum when the angle of projection is
A) 45 0
B) 30 0
C) 90 0
D) 60 0
136. A shell is fired from a gun barrel with a certain velocity will have maximum range if
fired with angle of ----- degrees with the horizontal plane.
A) 0 B) 30 C) 45 D) 90
137. A missile fired at an angle α to the horizontal hits a target. What should be the other
angle of projection to hit the same target, when initial velocity remains same?
A) 2 α B) 90 + α C) 90 – α D) 45 + α

Gaurav Burhade’s
STRUCTURE ACADEMY
Assignment
A) Curvilinear Motion
1. In curvilinear motion, the normal component of acceleration is
2. In curvilinear motion, the normal component of velocity is
3. When a particle is moving along a circular path with constant speed, the force acting
towards the centre of circle is
a) Centripetal force
b) Centrifugal force
c) Applied force
d) None of these
4. For a motion in a circular path , the radial component of velocity is
a) Equal to radius
b) Zero
c) Variable
d) Constant
5. In case of circular motion of a particle the tangential acceleration is equal to
6. When a stone is whirled in a vertical circle , the tension in the string is maximum at
a) The lowest point
b) The highest point
c) Mid height
d) 450
to the horizontal
7. A particle is moving along a curve and motion is defined by x=At3
and y=Bt3
. The speed
of the particle at any time ‘t’ is
8. The x and y coordinates of particle moving along a curve are x=2t2
+4 and y=3t+6. The
speed of particle at t=1 sec is

9. The motion of a particle is defined by x= 2 cos (πt) and y=1-4 cos (2πt). The path of
particle is
a) Parabola
b) Part of parabola
c) Hyperbola
d) None of these
10. If for a particle x-component of velocity is 10 m/s and y-component of velocity is 10 m/s.
the velocity in tangential direction is
11. If x=3 sin(t) and y=3 cos(t). the velocity of particle is
12. The radial axis is at an angle 450
with horizontal and tangential axis make 300
radial axis.
Velocity along transverse direction is 22 m/s. The value of r is
13. A particle is projected with velocity of 35 m/s at an angle of 300
with x- axis .The
component of acceleration in normal direction is
14. The magnitude of velocity is 25m/s at an angle of 300
with vertical. The normal
component of velocity is
15. The normal component of velocity is
a) Zero
b) Equal to velocity
c) Equal to speed
d) None of these
16. A particle moves along a path 3x+2y=5. The radius of curvature of the path at point
(1,1) is
17. A car starts from rest on a circular curve of radius 250 m and accelerates at a constant
tangential acceleration of 1.2 m/s2
.Time taken by car to attain total acceleration of 1.5
m/s2
is
18. A car moving at a constant speed of 36kmph enters a curved path of radius of curvature
100 m. The total acceleration of car is
19. The speed of a particle moving in a circle of radius r=2m varies with time t as v=t2
where
t is in sec and v in m/s. the net acceleration at t= 2 sec is

20. A particle moves in a circular path of radius 0.5 m with a linear speed of 2 m/s, find its
angular speed
21. A car of mass 1500 kg is moving with a speed of 12.5 m/s on a circular path of radius 20
m on a level road. What should be the value of coefficient of friction to attain the force?
22. A pendulum was kept horizontal and released. Find the acceleration of the pendulum.
When it makes an angle θ with the vertical
a) g√1+3cos2
θ
b) g√1+2cos2
θ
c) g sin θ
d) 2g cos θ
23. A coin placed on a rotating turn table just slips if it placed at a distance of 8 cm from
centre. If angular velocity of the turn table is doubled it will just slips at a distance of
24. A sphere of mass 0.2 kg is attached to an inextensible string of length 0.5 m whose upper
end is fixed on the ceiling. The sphere is made to describe a horizontal circle of radius 0.3
m. The speed of the sphere will be
25. The kinetic energy k of a particle moving along a circle of radius R depends on the
distance covered S as k=aS2
. The force acting on the particle is
26. A particle rests on the top of a hemisphere of radius R. Find the smallest horizontal
velocity that must be imparted to the particle if it is to leave the hemisphere without
sliding down it
27. A body of mass 5 kg is moving in a circle of radius 1 m with an angular velocity of 2
rad/sec. The centripetal force is
28. A body crosses the topmost vertical circle with critical speed. What will be its
acceleration, when the string is horizontal?
a) g b) 2g c) 3g d) 6g
29. A stone is tied at one end of a 5m long string & whirled in a vertical string. The min
speed required to cross the top most position is (g= 9.8m/sec2
)
30. A particle is placed at the highest point of a smooth sphere of radius r. it is given a slight
push, and is leaves the sphere at B, at a depth ‘h’ vertically bellow A such that h is equal
to
a) r/6 b) r/4 c) r/3 d) r/2

31. a body is to be slide without friction along an inclined plane of height h so that it loops
the loop of radius r at the bottom the value of the height is
a) h= 2r b) h= 4r c) h= 5r d) 5r/2
32. A car is moving along a circular arc at a speed of 20m/sec. the radius of the arc is 10m. if
the speed increased at the rate of 30m/sec2
. What is the resultant acceleration?
33. The acceleration of a train travelling with speed of 400m/s as it goes round a curve of
radius is :

B) Projectile motion
1. is For a projectile the velocity is minimum at
a) Projection point
b) Highest point
c) Striking point
d) At any other point
2. Maximum range of a projectile is
3. At a point of maximum height
a) Acceleration is zero
b) Velocity is zero
c) Both a) and b)
d) Velocity is along x-axis
4. If R=4H , the angle of projection is
5. Two particles are projected with same velocity but with different angles of projection for
same horizontal range. The possible angles are
6. The range of a projectile for given initial velocity of projector is minimum when angle of
projection is
7. When a projectile is projected from top of a building strikes the ground away from the
building then its horizontal distance is
a) Same as range
b) Less than range
c) More than range
d) None of these
8. If the two projectiles are fired with equal velocities but one with 300
and other at 600
then
both will have
a) Same time of flight
b) Equal horizontal range
c) Equal horizontal range as well as equal max. height
d) None of these
9. For a projectile of range R the K.E. is minimum after the projectile covers a distance is equal
to
a) R/4
b) R/2
c) R
d) 3R/4

10. A ball is thrown with 10 m/s at an angle of 600
with horizontal. The minimum velocity of
ball is
11. A bullet is fired with velocity of 200 m/s at an angle of 300
with horizontal. The bullet will
go vertically up to
12. 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
13. The range of a projectile fired at an angle of 150
is 50 m. If it is fired with the same speed at
an angle of 450
, its range will be
14. A man can throw a stone to a maximum distance of 80 m. The maximum height to which it
will rise in meter is
15. A body is projected with an initial velocity of (8i+6j) m/s. The horizontal range is (g=10 m/s)
16. A bomber plan moves horizontally with a speed of 500 m/s and a bomb released from it,
strikes the ground in 10 sec. Angle at which it strikes the ground will be (g=10m/s)
17. A monkey can jump a maximum horizontal distance of 20 m. Then the velocity of monkey is
18. A body is projected horizontally with a speed of 20 m/s. The approximate displacement of
the body after 5 sec is
19. A body is thrown with a velocity of 10 m/s at an angle of 600
with the horizontal. Its velocity
at highest point is
20. A cricket ball is hit at 300
with the horizontal with KE ‘E’. what is the KE at the highest
point?
21. The equation of a projectile is Y=√3x – (gx2
/2). The angle of projectile is given by
22. A projectile shot into air at some angle with the horizontal has a range of 200m. if the time of
flight is 5sec then the horizontal component of the velocity of the projectile at the highest
point of trajectory is
23. The KE of a projectile at the highest point is half of the initial KE. What is the angle of
projection with the horizontal?

24. The horizontal range of an oblique of projectile is equal to the distance through which
projectile has to fall freely from rest to acquire a velocity equal to velocity of projection in
magnitude. The angle of projection is
25. A particle is projected at an angle of 600
above the horizontal with the speed of 10m. After
sometime the direction of its velocity makes an angle of 300
above the horizontal. The speed
of the particle at this instant is
26. For a projectile the ratio of max height reached to the square of time of flight is (g=10m/s2
)
27. An object is projected at an angle of 450
with horizontal. The horizontal range and the max
height reached will be
28. A projectile can have the same range R for 2 angles of projection. If t1 & t2 be the times of
flights in the 2 cases, then the product of 2 time of flight is proportional to
a) R
b) 1/R
c) 1/R2
d) R2
29. 2 stones are projected with the same speeds but making different angles with the horizontal.
Their horizontal ranges are same. The angle of projection of 1 is π/3 the max height reached
by it is 102m. then the max height reached by other in meter is

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