R4RIN – MCQs, Mock Tests | IIT JEE IIT JEE Circular Motion Centre Of Mass

A wheel is at rest. Its angular velocity increases uniformly and becomes 80 rad/s after 5s. The total angular displacement is:

1. 800 rad
2. 400 rad
3. 200 rad
4. 100 rad

✅ Correct Answer: 3

A national roadway bridge over a canal is in the form of an arc of a circle of radius 49 m. What is the maximum speed with which a car can move without leaving the ground at the highest point? (Take g = 9.8 m/second square)

1. 19.6 m/s
2. 40 m/s
3. 22 m/s
4. none of these

✅ Correct Answer: 3

A car of 1400 kg is moving on a circular path of radius 30 m with a speed of 40 km/h. When the driver applies the brakes and the car continues to move along the circular path, what is the maximum deceleration possible if the tyres are limited to a total horizontal friction of 10.6 kN?

1. 10 m/second square
2. 6.36 m/second square
3. 4 m/second square
4. none of these

✅ Correct Answer: 2

A heavy stone hanging from a massless string of length 15 m is projected horizontally with speed 147 m/s. The speed of the particle at the point where the tension in the string equals the weight of the particle is:

1. 10 m/s
2. 7 m/s
3. 12 m/s
4. none of these

✅ Correct Answer: 3

A car travels with a uniform velocity in north direction. It goes over a piece of mud which sticks to the tyre, the particles of the mud, as it leaves the ground are thrown:

1. vertically downward
2. vertically upward
3. horizontally to north
4. horizontally to south

✅ Correct Answer: 4

A curved section of a rod is banked for a speed v. If there is no friction between road and tyres of the car, than:

1. car is more likely to slip at speeds higher than v than speeds lower than v
2. car cannot remain in static equilibrium on the curved section
3. car will not slip when moving with speed v
4. none of the above

✅ Correct Answer: 3

A motor cyclist rides around the well with a round vertical wall and does not fall down while riding because:

1. the force of gravity disappears
2. he loses weight some how
3. he is kept in this path due to the force exerted by surrounding air
4. the frictional force of the wall balances his weight

✅ Correct Answer: 4

A projectile is projected at an angle 60 degree with horizontal with speed 10 m/s. The minimum radius of curvature of the trajectory described by the projectile is:

1. 2.55 m
2. 2 m
3. 10 m
4. none of these

✅ Correct Answer: 1

A particle of mass 100 g tied to a string is rotated along a circle of radius 0.5 m. The breaking tension of string is 10N. The maximum speed with which particle can be rotated without breaking the string is:

1. 10 m/s
2. 9.8 m/s
3. 7.7 m/s
4. 7.07 m/s

✅ Correct Answer: 4

When a body moves with constant speed in a circular path, then:

1. work done will be zero
2. acceleration will be zero
3. no force acts on a body
4. its velocity remains constant

✅ Correct Answer: 3

A stone of mass 0.3 kg attached to a 1.5 m long string is whirled around in a horizontal circle at a speed of 6 m/s. The tension in the string is:

1. 10N
2. 20N
3. 7.2 N
4. none of these

✅ Correct Answer: 3

Which of the following statements is false for a particle moving in a circle with a constant angular speed?

1. The velocity vector is tangent to the circle
2. The acceleration vector is tangent to the circle
3. The acceleration vector points to the centre of the circle
4. The velocity and acceleration vectors are perpendicular to each other

✅ Correct Answer: 2

Which of the following statements about the centripetal and centrifugal forces is correct?

1. Centripetal force balances the centrifugal force
2. Both centripetal force and centrifugal force act on the same body
3. Centripetal force is directed opposite to the centrifugal force
4. Centripetal force is experienced by the observer at the centre of the circular path described by the bod

✅ Correct Answer: 3

The string of a pendulum is horizontal. The mass of bob attached to it is m. Now the string is released. The tension in the string in the lowest position, is:

1. mg
2. 2 mg
3. 3 mg
4. 4 mg

✅ Correct Answer: 3

Let ? denote the angular displacement of a simple pendulum oscillating in a vertical plane If the mass of the bob is m, the tension in the string is mg cos ?:

1. always
2. never
3. at the extreme positions
4. at the mean position

✅ Correct Answer: 3

A stone of mass 1 kg is tied at one end of string of length 1m It is whirled in a vertical circle at constant speed of 4 m/s The tension in the string is 6N when the stone is at: (g = 10 m/second square)

1. top of the circle
2. bottom of the circle
3. half way down
4. none of these

✅ Correct Answer: 1

The speed of a particle moving in a circle is increasing. The dot product of its acceleration and velocity is:

1. negative
2. zero
3. positive
4. may be +ve or ?ve

✅ Correct Answer: 3

A car moving on a horizontal road may be thrown out of the road in taking a turn:

1. by a gravitational force
2. due to lack of proper centripetal force
3. due to the rolling frictional force between the tyre and road
4. due to the reaction of the ground

✅ Correct Answer: 2

A small body of mass m slides down from the top of a hemisphere of radius R. The surface of block and hemisphere are frictionless. The height at which the body loses contact with the surface of the sphere is:

1. 3/2 R
2. 2/3 R
3. 1/2 R
4. 1/3 R

✅ Correct Answer: 2

When a simple pendulum is rotated in a vertical plane with constant angular velocity, centripetal force is:

1. maximum at highest point
2. maximum at lowest point
3. same at all points
4. zero

✅ Correct Answer: 3

Mark correct option or options from the following

1. In the case of circular motion of a particle, centripetal force may be balanced by centrifugal force
2. In the non-inertial reference frame centrifugal force is real force
3. In the inertial reference frame, centrifugal force is real force
4. Centrifugal force is always pseudo force

✅ Correct Answer: 3

A stone of mass 1 kg is tied to the end of a string 1 m long It is whirled in a vertical circle The velocity of the stone at the bottom of the circle is just sufficient to take it to the top of circle without slackening of the string What is the tension in the string at the top of the circle? (Take g = 10 m/s)

1. Zero
2. 1N
3. v10N
4. 10N

✅ Correct Answer: 1

A particle is acted upon by a force of constant magnitude which is always perpendicular to the velocity of the particle. The motion of the particle takes place in a plane. It follows that:

1. its velocity is constant
2. its acceleration is constant
3. its kinetic energy is constant
4. it does not move on a circular path

✅ Correct Answer: 3

The maximum speed with which an automobile can round a curve of radius 8 m without slipping if the road is unbanked and the co-efficient of friction between the road and the tyres is 0.8, is: (g = 10 m/second square)

1. 8 m/s
2. 10 m/s
3. 20 m/s
4. none of these

✅ Correct Answer: 1

A stone of mass m tied to a string of length l is rotated in a circle with the other end of the string as the centre. The speed of the stone is v. If the string breaks, the stone will:

1. move towards the centre
2. move away from the centre
3. move along a tangent
4. stop

✅ Correct Answer: 3

In circular motion:

1. radial acceleration is non-zero
2. radial velocity is zero
3. body is in equilibrium
4. all of the above

✅ Correct Answer: 4

A coin placed on a rotating turntable just slips if it is placed at a distance of 8 cm from the centre. If angular velocity of the turntable is doubled, it will just slip at a distance of:

1. 1 cm
2. 2 cm
3. 4 cm
4. 8 ccm

✅ Correct Answer: 2

A chain of 125 links is 125 m long and has a mass of 2 kg with the ends fastened together It is set for rotating at 50 rev/s, the centripetal force on each link is:

1. 3.14 N
2. 0.314 N
3. 314 N
4. none of these

✅ Correct Answer: 3

A body is rolling without slipping on a horizontal plane. The rotational energy of the body is 40% of the total kinetic energy. Identify the body.

1. Ring
2. Hollow cylinder
3. Solid cylinder
4. Hollow sphere

✅ Correct Answer: 4

he diameter of a flywheel increases by 1%. The percentage increase in moment of inertia about its axis passing through the centre will be

1. 2%
2. 2.50%
3. 1.50%
4. 3%

✅ Correct Answer: 1

The angular momentum changes from 2 units to 6 units in 4 s. The torque is

1. 1 unit
2. 1 / 2 unit
3. 3/ 2 unit
4. 4 unit

✅ Correct Answer: 1

A particle performs uniform circular motion with an angular momentum L. If the frequency of particle s motion is doubled and its kinetic energy is halved, then the angular momentum becomes

1. L / 2
2. L / 4
3. L / 6
4. L / 8

✅ Correct Answer: 4

A mass m is moving with a constant velocity parallel to the x -axis. Its angular momentum w. r. t. the origin

1. remains constant
2. goes on increasing
3. goes on decreasing
4. is zero

✅ Correct Answer: 1

A body crosses the topmost point of a vertical circle with critical speed. What will be its acceleration when the string is horizontal ?

1. g
2. 2g
3. 3g
4. 6g

✅ Correct Answer: 3

A sphere is rolling without slipping on a horizontal plane. The ratio of its rotational kinetic energy and translational kinetic energy is

1. 2:03
2. 2:05
3. 2:07
4. 2:09

✅ Correct Answer: 2

Which of the following is conserved when the torque acting on a system is zero ?

1. K.E.
2. Angular momentum
3. Angular K.E
4. Linear momentum

✅ Correct Answer: 2

If the Earth shrinks to half of the present radius, without any change in mass, then the duration of day and night becomes

1. 24 hours
2. 12 hours
3. 6 hours
4. 3 hours

✅ Correct Answer: 3

A body rolls down an inclined plane If its kinetic energy of rotational motion is 40% of its kinetic energy of translation, then the body is

1. ring
2. solid sphere
3. solid disc
4. cylinder

✅ Correct Answer: 2

Two wheels, each with four spokes, are mounted one behind the other and aligned such that an observer sees only four spokes At t =0 minute, one wheel begins to spin at 5 revolutions/ minute and the other at 4 revolutions / minute Upto t = 1 minute, how many times the observer would see only four spokes ?

1. 1
2. 2
3. 4
4. 8

✅ Correct Answer: 3

A particle is projected so as to just move along a vertical circle. The ratio of the tensions in the string when the particle is at the lowest and highest point on the circle is

1. 1
2. finite but large
3. zero
4. infinite

✅ Correct Answer: 4

A rigid spherical body is spinning around an axis without any external torque Due to change in temperature, the volume increases by 1% The angular speed will approximately

1. increase by 1%
2. decrease by 1%
3. decrease by 0.67%
4. decrease by 0.33%

✅ Correct Answer: 3

When a sphere rolls without slipping the ratio of kinetic energy of translation to its total kinetic energy is

1. 1:07
2. 1:02
3. 1:01
4. 5:07

✅ Correct Answer: 4

A coin placed on a rotating turntable just slips if it is placed at a distance of 4 cm from the center If the angular velocity of the turntable is doubled, it will just slip at a distance of

1. 1 cm
2. 2 cm
3. 4 cm
4. 8 ccm

✅ Correct Answer: 1

Radius of gyration of a body about an axis at a distance of 6 cm from its centre of mass is 10 cm, The radius of gyration about a parallel axis through its centre of mass is

1. 2 cm
2. 4 cm
3. 8 cm
4. 12 cm

✅ Correct Answer: 3

If the angular momentum of a body increases by 50%, its kinetic energy of rotation increases by

1. 50%
2. 125%
3. 200%
4. 100%

✅ Correct Answer: 2

A child stands at the centre of a turn table with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. Now, the child folds his hands back and thereby reduces his moment of inertia to 2 / 5 times the initial value. The new kinetic energy of rotation. The value of x is

1. 2.5
2. 5
3. 1
4. 6.756

✅ Correct Answer: 1

The moment of inertia of uniform circular disc about a diameter is I. Its moment of inertia about an axis perpendicular to its plane and passing through a point on its rim will be

1. 21
2. 41
3. 61
4. 81

✅ Correct Answer: 3

The string of a pendulum is horizontal. The mass of the bob attached to it is m. Now the string is released. The tension in the string in the lowest position is

1. mg
2. 2mg
3. 3mg
4. 4mg

✅ Correct Answer: 3

A coin placed on a gramophone record rotating at 33 r p m files off the record, if it is placed at a distance of more than 16 cm from the axis of rotation If the record is revolving at 66 r p m, the coin will fly off if it is placed at a distance not less than

1. 1 cm
2. 2 cm
3. 3 cm
4. 4cm

✅ Correct Answer: 4

The masses of two uniform discs are in the ratio 1 : 2 and their diameters in the 2 : 1 The ratio of their moments of inertia about the axes passing through their respective centres and perpendicular to their planes is

1. 1:01
2. 1:02
3. 2:01
4. 1:04

✅ Correct Answer: 3

A nearly massless rod is pivoted at one end so that it can swing freely as a pendulum Two masses 2m and m are attached to it at distance b and 3b respectively from the pivot The rod is held horizontal and then released The angular acceleration of the rod at the instant it is released is

1. bg
2. b/g
3. gb+5
4. 5g / 11b

✅ Correct Answer: 4

A chain of 125 links is 1.25 m long and has a mass of 2 kg. With the ends fastened together, it is set rotating at 3000 rev/ min. The centripetal force on each link is

1. 3.14 N
2. 1 / 3.14 N
3. 1 / 314 N
4. none of these

✅ Correct Answer: 2

A disc-like reel with massless thread unrolls itself while falling vertically downwards The acceleration of its fall is

1. zero
2. goes on increasing
3. 2/3 g
4. g/2

✅ Correct Answer: 3

Two solid spheres are made of the same material. The ratio of their diameters is 1 : 2. The ratio of their moments of inertia about their respective diameters is

1. 1:01
2. 1:04
3. 1:16
4. 1:32

✅ Correct Answer: 4