Assignment: Circular Motion
1. Exercise 1
EXERCISE-1
CIRCULAR MOTION
Q. 1 The angle between velocity vector and acceleration vector in uniform circular motion is
(1)
(2)
(3)
(4)
Q. 2 Two cyclists cycle along circular tracks of radii and at uniform rates. If both of then take same time to complete one revolution, then their angular speeds are in the ratio
(1)
(2)
(3)
(4)
Q. 3 Angular speed of a uniformly circulating body with time period is
(1)
(2)
(3)
(4)
Q. 4 An object moving in a circular path at constant speed has constant
(1) Energy
(2) Velocity
(3) Acceleration
(4) Displacement
Q. 5 Speed of an object moving in circular path of radius with angular speed is
(1)
(2)
(3)
(4)
Q. 6 A wheel is at rest. Its angular velocity increases uniformly and becomes 160 radian per second after 5 second. The total angular displacement is :
(1)
(2)
(3)
(4)
Q. 7 Two wheels having radii in the ratio are connected by a common belt. If the smaller wheel is accelerated from rest at a rate for . The velocity of bigger wheel is
(1)
(2)
(3)
(4) None of these
.
Q. 8 A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle in the first , in the next , it rotates through an additional angle , the ratio of is
(1) 1
(2) 2
(3) 3
(4) 5
Q. 9 When a particle moves in a circle with a uniform speed
(1) its velocity and acceleration are both constant
(2) its velocity is constant but the acceleration changes
(3) its acceleration is constant but the velocity changes
(4) its velocity and acceleration both change
Q. 10 The relation between an angular velocity, the position vector and linear velocity of a particle moving in a circular path is.
(1)
(2)
(3)
(4)
Q. 12 The angular speed of a fly wheel making 120 revolutions/minute is.
(1)
(2)
(3)
(4)
Q. 13 The angular velocity of the second's needle in watch is-
(1)
(2)
(3)
(4)
Q. 14 The average acceleration vector in one revolution for a particle having a uniform circular motion is-
(1) A constant vector of magnitude
(2) A vector of magnitude directed normal to the plane of the given uniform circular motion.
(3) Equal to the instantaneous acceleration vector at the start of the motion.
(4) Anull vector.
Q. 15 A body performing uniform circular motion completed 140 revolution in a second. Its angular speed is
(1)
(2)
(3)
(4)
Q. 16 Centripetal acceleration of a cyclist completing 7 rounds in a minute along a circular track of radius with a constant speed, is
(1)
(2)
(3)
(4)
Q. 17 An aircraft executes a horizontal loop of radius with a speed of . Ratio of centripetal acceleration to acceleration due to gravity is
(1) 12.3
(2) 3.3
(3) 6.4
(4) None of these
Q. 18 If the frequency of an object in uniform circular motion is doubled, its acceleration becomes
(1) Two times
(2) Four times
(3) Half
(4) One fourth
Q. 19 A body is moving on a circle of radius with a seed which is decreasing at the rate at an instant. The angle made by its acceleration with its velocity is
(1)
(2)
(3)
(4)
Q. 20 The distance of a particle moving on a circle of radius measured from a fixed point on the circle and measured along the circle is given by (in meters). The ratio of its tangential to centripetal acceleration at is
(1)
(2)
(3)
(4)
Q. 21 A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle as , where and are positive constants. At the moment , the time dependence of rotation angle is
(1)
(2)
(3)
(4)
.
Q. 22 Two particles and are located at distances and respectively from the axis of a rotating disc such that :
(1) Both and have the same acceleration
(2) Both and do not have any acceleration
(3) P has greater acceleration than
(4) has greater acceleration than
Q. 23 Let and represent radial and tangential acceleration. The motion of a particle may be circular if:
(1)
(2)
(3)
(4) none of these
Q. 24 Astring breaks if its tension exceeds 10 newtons. A stone of mass 250 gm tied to this string of length 10 is rotated in a horizontal circle. The maximum angular velocity of rotation can be.
(1)
(2)
(3)
(4)
Q. 25 A particle moving along a circular path due to a centripetal force having constant magnitude is an example of motion with:
(1) constant speed and velocity
(2) variable speed and velocity
(3) variable speed and constant velocity
(4) constant speed and variable velocity.
Q. 26 The formula for centripetal acceleration in a circular motion is.
(1)
(2)
(3)
(4)
Q. 27 A stone is moved round a horizontal circle with a long string tied to it. If centripetal acceleration is , then its angular velocity will be
(1)
(2)
(3)
(4)
Q. 28 A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance ' '. The speed of the particle is.
(1) Proportional to
(2) Independent of
(3) Proportional to
(4) Proportional to
Q. 29 A particle of mass is moving in a horizontal circle of radius under a centripetal force equal to . The total kinetic energy of the particle is-
(1)
(2)
(3)
(4)
Q. 30 A particle of mass is moving with constant velocity on smooth horizontal surface. A constant force starts acting on particle perpendicular to velocity . Radius of curvature after force start acting is :
(1)
(2)
(3)
(4) none of these
Q. 31 If the radii of circular paths of two particles of same masses are in the ratio of , then in order to have same centripetal force, their speeds should be in the ratio of:
(1)
(2)
(3)
(4)
Q. 32 A particle is moving in a horizontal circle with constant speed. It has constant
(1) Velocity
(2) Acceleration
(3) Kinetic energy
(4) Displacement
Q. 33 The tension in the string revolving in a vertical circle with a mass at the end when it is at the lowest position.
(1)
(2)
(3)
(4)
Q. 34 A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it :
(1) increase
(2) decreases
CIRCULAR MOTION
Q. 1 The angle between velocity vector and acceleration vector in uniform circular motion is
(1)
(2)
(3)
(4)
Q. 2 Two cyclists cycle along circular tracks of radii
(1)
(2)
(3)
(4)
Q. 3 Angular speed of a uniformly circulating body with time period
(1)
(2)
(3)
(4)
Q. 4 An object moving in a circular path at constant speed has constant
(1) Energy
(2) Velocity
(3) Acceleration
(4) Displacement
Q. 5 Speed of an object moving in circular path of radius
(1)
(2)
(3)
(4)
Q. 6 A wheel is at rest. Its angular velocity increases uniformly and becomes 160 radian per second after 5 second. The total angular displacement is :
(1)
(2)
(3)
(4)
Q. 7 Two wheels having radii in the ratio
(1)
(2)
(3)
(4) None of these
.
Q. 8 A car wheel is rotated to uniform angular acceleration about its axis. Initially its angular velocity is zero. It rotates through an angle
(1) 1
(2) 2
(3) 3
(4) 5
Q. 9 When a particle moves in a circle with a uniform speed
(1) its velocity and acceleration are both constant
(2) its velocity is constant but the acceleration changes
(3) its acceleration is constant but the velocity changes
(4) its velocity and acceleration both change
Q. 10 The relation between an angular velocity, the position vector and linear velocity of a particle moving in a circular path is.
(1)
(2)
(3)
(4)
Q. 11 A wheel is of diameter . If it makes 30 revolutions/sec., then the linear speed of a point on its circumference will be.
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
Q. 12 The angular speed of a fly wheel making 120 revolutions/minute is.
(1)
(2)
(3)
(4)
Q. 13 The angular velocity of the second's needle in watch is-
(1)
(2)
(3)
(4)
Q. 14 The average acceleration vector in one revolution for a particle having a uniform circular motion is-
(1) A constant vector of magnitude
(2) A vector of magnitude
(3) Equal to the instantaneous acceleration vector at the start of the motion.
(4) Anull vector.
Q. 15 A body performing uniform circular motion completed 140 revolution in a second. Its angular speed is
(1)
(2)
(3)
(4)
Q. 16 Centripetal acceleration of a cyclist completing 7 rounds in a minute along a circular track of radius
(1)
(2)
(3)
(4)
Q. 17 An aircraft executes a horizontal loop of radius
(1) 12.3
(2) 3.3
(3) 6.4
(4) None of these
Q. 18 If the frequency of an object in uniform circular motion is doubled, its acceleration becomes
(1) Two times
(2) Four times
(3) Half
(4) One fourth
Q. 19 A body is moving on a circle of radius
(1)
(2)
(3)
(4)
Q. 20 The distance of a particle moving on a circle of radius
(1)
(2)
(3)
(4)
Q. 21 A solid body rotates about a stationary axis so that its angular velocity depends on the rotational angle
(1)
(2)
(3)
(4)
.
Q. 22 Two particles
(1) Both
(2) Both
(3) P has greater acceleration than
(4)
Q. 23 Let
(1)
(2)
(3)
(4) none of these
Q. 24 Astring breaks if its tension exceeds 10 newtons. A stone of mass 250 gm tied to this string of length 10
(1)
(2)
(3)
(4)
Q. 25 A particle moving along a circular path due to a centripetal force having constant magnitude is an example of motion with:
(1) constant speed and velocity
(2) variable speed and velocity
(3) variable speed and constant velocity
(4) constant speed and variable velocity.
Q. 26 The formula for centripetal acceleration in a circular motion is.
(1)
(2)
(3)
(4)
Q. 27 A stone is moved round a horizontal circle with a
(1)
(2)
(3)
(4)
Q. 28 A particle moves in a circular orbit under the action of a central attractive force inversely proportional to the distance '
(1) Proportional to
(2) Independent of
(3) Proportional to
(4) Proportional to
Q. 29 A particle of mass
(1)
(2)
(3)
(4)
Q. 30 A particle of mass
(1)
(2)
(3)
(4) none of these
Q. 31 If the radii of circular paths of two particles of same masses are in the ratio of
(1)
(2)
(3)
(4)
Q. 32 A particle is moving in a horizontal circle with constant speed. It has constant
(1) Velocity
(2) Acceleration
(3) Kinetic energy
(4) Displacement
Q. 33 The tension in the string revolving in a vertical circle with a mass
(1)
(2)
(3)
(4)
Q. 34 A motorcycle is going on an overbridge of radius R. The driver maintains a constant speed. As the motorcycle is ascending on the overbridge, the normal force on it :
(1) increase
(2) decreases
Q. 35 In a circus, stuntman rides a motorbike in a circular track of radius in the vertical plane. The minimum speed at highest point of track will be :
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
Q. 36 A particle is moving in a vertical circle. The tensions in the string when passing through two positions at angles and from vertical (lowest positions) are and respectively. Then
(1)
(2)
(3)
(4) Tension in the string always remains the same
(1)
(2)
(3)
(4) Tension in the string always remains the same
Q. 37 A stone tied to a string is rotated in a vertical plane. If mass of the stone is , the length of the string is and the linear speed of the stone is when the stone is at its lowest point, then the tension in the string at the lowest point will be :
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
Q. 38 A car moves at a constant speed on a road as shown in figure. The normal force by the road on the car is and when it is at the points and respectively.
Q. 39 A stone of mass attached to a long string is whirled around in a horizontal circle at a speed of . The tension in the string is
(1)
(2)
(3)
(4) None of these
(1)
(2)
(3)
(4) None of these
Q. 40 A stone of mass is tied to a string long and is rotated at constant speed of in a vertical circle. The ratio of the tension at the top and the bottom is (Take, )
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
Q. 41 A heavy stone hanging from a massless string of length is projected horizontally with speed . The speed of the particle at the point where the tension in the string equals the weight of the particle is
(1)
(2)
(3)
(4) None of these
(1)
(2)
(3)
(4) None of these
Q. 42 A coin placed on a rotating turn table just slips, if it is placed at a distance of from the centre. If angular velocity of the turn table is doubled, it will just slip at a distance of
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)
Q. 43 A man stands in contact against the inner wall of a hollow cylindrical drum of radius rotating about its vertical axis with . The coefficient of friction between the wall and his clothing is 0.15 . When the floor is suddenly removed, what is the minimum rotational speed of the cylinder to enable the man to remain stuck to the wall without falling (approximately)?
(1)
(2)
(3)
(4)
(1)
(2)
(3)
(4)