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A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A plumb bob is suspended from the roof of the car by a light rigid rod of length 10 m. The angle made by the rod with the track is
(Take g = 10m/s2)

0°

30°

45°

60°

The angle of bank provided on road depends upon

mass of the vehicle

nature of the road surface

velocity with which the vehicle is negotiating the bend

position of centre of gravity of the vehicle

frictional resistance between the road and tyre

A spherical cage of radius 5 m has been erected for performing a motor cycle feat of ‘going in a vertical circle’. The minimum speed with which the cyclist should perform the feat so that he may not fall is a about (Take g = 9.8 ms2)

4.95 m/s

7.0 m/s

9.9 m/s

13.85 m/s

A train running at 48 km/hr has to negotiate a curve of 400 m radius. If the distance between the rails is 1 m, by how much should the outer rail be raised with respect to the inner rail? (Take g = 10m/s2)

2.22 cm

4.44 cm

6.66 cm

8.88 cm

An aero plane traveling at a speed of 600 km/hr banks at an angle of 30 degree as it makes a turn. The radius of curve is about (Take g = 10 m/s2)

3.4 km

4.8 km

2 km

8.6 km

A motor cyclist goes around a circular track of 440 m length in 20 seconds. The cyclist should then make an angle with the vertical equal to about( Take g = 9.8 m/s2 )

18°

35°

47°

59°

Which of the following is a wrong statement regarding banking; the system of providing an inclination for the road on curve?

The inclination slopes upwards towards the outer circumference

The force of friction between the wheels and the road provides the centripetal force

banking reduces the wearing out of the tires

Banking prevents the centrifugal force from throwing the vehicle away from the road

A body of mass m attached to a string of length l constitutes a simple pendulum. At the instant when the bob acquires maximum speed v while executing simple harmonic motion, the tension in the string equals

mg + mv2

mg + mv2/2l

mg + mv2/l

mg + 2 mv2/l

Mark the statement that does not conform to circular motion :

The magnitude of velocity remains the same but there occurs a change in the direction of velocity vector

The direction of velocity vector at any point on the circular orbit in along the tangent to the circle at that point

The acceleration experienced by the particle lies perpendicular to the velocity vector and hence along the radius directed towards the centre

When the string of a ball being whirled in a circle is released, the centripetal force on the ball ceases to act and the ball flies off along the radius

A solid sphere rolls on a level surface. The rotational kinetic energy and total kinetic energy are in the ratio

2 : 7

5 : 7

3 : 7

1 : 3

A solid sphere of mass m and radius r rolls, without slipping, with uniform velocity V along straight line on a horizontal table. The total energy will be

2/5 mV2

5/6 mV2

7/10 mV2

3/8 mV2

A ring (mass 0.3 kg and radius 0.1 m) and a solid cylinder (mass 0.4 kg and radius 0.1 m) are given the same kinetic energy and released simultaneously on a flat horizontal surface such that they begin to roll towards a wall which is at the same distance from the ring and cylinder. If the rolling friction is negligible, then :

cylinder will reach the wall first

ring will reach the wall first

both will reach the wall at the same time

date is insufficient to make any prediction

A particle covers equal distances around a circular path in equal intervals of time. Which of the following parameters connected with the motion of particle remains constant with time?

displacement

speed

velocity

acceleration

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 the particle has

motion in a circular path

constant velocity

constant acceleration

constant kinetic energy

A particle is moving along a circular path with uniform speed. The force acting on the particle is

zero

constant is magnitude only

continuously varying in magnitude and direction

constant both in magnitude and direction

For a particle moving in a circular orbit of radius 0.4 m, the angular velocity and angular acceleration at a particular instant are 2rad/s and 5rad/s2. The particle then has a total linear acceleration of

1.9 m/s2

2.69 m/s2

3.8 m/s2

7.24 m/s2

An aircraft executes a horizontal loop of radius 1 km with a steady speed of 900 km/hr. In terms of acceleration due to gravity (g = 10 m/s2), the centripetal acceleration of aircraft would be

3.12 g

6.25 g

12.5 g

18.75 g

Starting from rest, a particle travels on a circular path and the distance covered is prescribed by the relation s = kt2; where k is constant and t is the time. The particle then has a tangential acceleration of

k/2

k

2k

4k

A stone tied to the end of a string 1000 cm ling is whirled in a horizontal circle with a constant speed. If the stone makes 15 revolutions in 30 seconds, the acceleration of the stone is closest to

315 cm/s2

630 cm/s2

985 cm/s2

3950 cm/s2

A person standing on a uniformly rotating turn table has his arms held close to his chest. If he outstretches his arms

the moment of inertia will decrease

the angular momentum will increase

the speed of rotation will decrease

the angular velocity will remain constant

Which of the following units do not conform to the concept of rigid body rotation?

blades of a fan

pulley of a belt

phonograph records

door revolving about a hinge

wheels of an automobile

The flywheel of a system of a steam engine has a radius of gyration of 1 m and a mass of 2500 kg. The starting torque of the engine is 1500 Nm and remains constant. The angular acceleration of the flywheel is

0.6 rad/s2

0.83 rad/s2

1.2 rad/s2

1.67 rad/s2

A rotating body needs a torque of 2 * 10-4 Nm to acquire an angular acceleration of 4 rad/s2. The moment of inertia of the body is

0.25 * 10-4 kg m2

0.5 * 10-4 kg m2

0.75 * 10-4 kg m2

1.0 * 10-4 kg m2

A ring of mass 10 kg and diameter 0.4 m is made to turn 2100 rev/min about its axis. The ring will then have an angular momentum of

44 kgm2/s2

88 kgm2/s2

132 kgm2/s2

176 kgm2/s2

A body moving around a fixed axis constitutes :

rotational motion

circular motion

plane motion

simultaneous translation and rotation

A stone is whirled in a vertical circle. The tension in the string would be greatest when the stone is

in the highest position

in the lowest position

in a position when it is horizontal

tension remains same in all the positions

A ball weighing 0.14 kg is being whirled in a horizontal circle at the end of a string 0.5 m long. If the breaking tension of the string is 35 N, the maximum angular velocity with which the stone can be whirled is approximately___________

12.9 rad/s

15.8 rad/s

22.4 rad/s

31.6 rad/s

A body of mass 1 kg is attached to a string 1 m long and is whirled in a horizontal circle. If the string ca withstand a tension of 25 N, the maximum whirling speed can be

5 m/s

6.8 m/s

9.5 m/s

12.5 m/s

The rotational analogue of force in linear motion is

couple

torque

moment of momentum

moment of inertia

A zero torque acting on a system will result in conversation of

linear velocity

angular velocity

angular momentum

moment of momentum

An attempt to turn a key into a lock manifests in the application of

coplanar force

moment

couple

torque

Mark the wrong statement

The constituent particles of a rigid body retain their relative positions even in motion

Torque is necessary to change the angular velocity of a rotating body

In the absence of an external torque, the angular velocity of the system is conserved

Moment of inertia is the analogue of mass in linear motion

0°

30°

45°

60°

The angle of bank provided on road depends upon

mass of the vehicle

nature of the road surface

velocity with which the vehicle is negotiating the bend

position of centre of gravity of the vehicle

frictional resistance between the road and tyre

A spherical cage of radius 5 m has been erected for performing a motor cycle feat of ‘going in a vertical circle’. The minimum speed with which the cyclist should perform the feat so that he may not fall is a about (Take g = 9.8 ms2)

4.95 m/s

7.0 m/s

9.9 m/s

13.85 m/s

A train running at 48 km/hr has to negotiate a curve of 400 m radius. If the distance between the rails is 1 m, by how much should the outer rail be raised with respect to the inner rail? (Take g = 10m/s2)

2.22 cm

4.44 cm

6.66 cm

8.88 cm

An aero plane traveling at a speed of 600 km/hr banks at an angle of 30 degree as it makes a turn. The radius of curve is about (Take g = 10 m/s2)

3.4 km

4.8 km

2 km

8.6 km

A motor cyclist goes around a circular track of 440 m length in 20 seconds. The cyclist should then make an angle with the vertical equal to about( Take g = 9.8 m/s2 )

18°

35°

47°

59°

Which of the following is a wrong statement regarding banking; the system of providing an inclination for the road on curve?

The inclination slopes upwards towards the outer circumference

The force of friction between the wheels and the road provides the centripetal force

banking reduces the wearing out of the tires

Banking prevents the centrifugal force from throwing the vehicle away from the road

A body of mass m attached to a string of length l constitutes a simple pendulum. At the instant when the bob acquires maximum speed v while executing simple harmonic motion, the tension in the string equals

mg + mv2

mg + mv2/2l

mg + mv2/l

mg + 2 mv2/l

Mark the statement that does not conform to circular motion :

The magnitude of velocity remains the same but there occurs a change in the direction of velocity vector

The direction of velocity vector at any point on the circular orbit in along the tangent to the circle at that point

The acceleration experienced by the particle lies perpendicular to the velocity vector and hence along the radius directed towards the centre

When the string of a ball being whirled in a circle is released, the centripetal force on the ball ceases to act and the ball flies off along the radius

A solid sphere rolls on a level surface. The rotational kinetic energy and total kinetic energy are in the ratio

2 : 7

5 : 7

3 : 7

1 : 3

A solid sphere of mass m and radius r rolls, without slipping, with uniform velocity V along straight line on a horizontal table. The total energy will be

2/5 mV2

5/6 mV2

7/10 mV2

3/8 mV2

A ring (mass 0.3 kg and radius 0.1 m) and a solid cylinder (mass 0.4 kg and radius 0.1 m) are given the same kinetic energy and released simultaneously on a flat horizontal surface such that they begin to roll towards a wall which is at the same distance from the ring and cylinder. If the rolling friction is negligible, then :

cylinder will reach the wall first

ring will reach the wall first

both will reach the wall at the same time

date is insufficient to make any prediction

A particle covers equal distances around a circular path in equal intervals of time. Which of the following parameters connected with the motion of particle remains constant with time?

displacement

speed

velocity

acceleration

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 the particle has

motion in a circular path

constant velocity

constant acceleration

constant kinetic energy

A particle is moving along a circular path with uniform speed. The force acting on the particle is

zero

constant is magnitude only

continuously varying in magnitude and direction

constant both in magnitude and direction

For a particle moving in a circular orbit of radius 0.4 m, the angular velocity and angular acceleration at a particular instant are 2rad/s and 5rad/s2. The particle then has a total linear acceleration of

1.9 m/s2

2.69 m/s2

3.8 m/s2

7.24 m/s2

An aircraft executes a horizontal loop of radius 1 km with a steady speed of 900 km/hr. In terms of acceleration due to gravity (g = 10 m/s2), the centripetal acceleration of aircraft would be

3.12 g

6.25 g

12.5 g

18.75 g

Starting from rest, a particle travels on a circular path and the distance covered is prescribed by the relation s = kt2; where k is constant and t is the time. The particle then has a tangential acceleration of

k/2

k

2k

4k

A stone tied to the end of a string 1000 cm ling is whirled in a horizontal circle with a constant speed. If the stone makes 15 revolutions in 30 seconds, the acceleration of the stone is closest to

315 cm/s2

630 cm/s2

985 cm/s2

3950 cm/s2

A person standing on a uniformly rotating turn table has his arms held close to his chest. If he outstretches his arms

the moment of inertia will decrease

the angular momentum will increase

the speed of rotation will decrease

the angular velocity will remain constant

Which of the following units do not conform to the concept of rigid body rotation?

blades of a fan

pulley of a belt

phonograph records

door revolving about a hinge

wheels of an automobile

The flywheel of a system of a steam engine has a radius of gyration of 1 m and a mass of 2500 kg. The starting torque of the engine is 1500 Nm and remains constant. The angular acceleration of the flywheel is

0.6 rad/s2

0.83 rad/s2

1.2 rad/s2

1.67 rad/s2

A rotating body needs a torque of 2 * 10-4 Nm to acquire an angular acceleration of 4 rad/s2. The moment of inertia of the body is

0.25 * 10-4 kg m2

0.5 * 10-4 kg m2

0.75 * 10-4 kg m2

1.0 * 10-4 kg m2

A ring of mass 10 kg and diameter 0.4 m is made to turn 2100 rev/min about its axis. The ring will then have an angular momentum of

44 kgm2/s2

88 kgm2/s2

132 kgm2/s2

176 kgm2/s2

A body moving around a fixed axis constitutes :

rotational motion

circular motion

plane motion

simultaneous translation and rotation

A stone is whirled in a vertical circle. The tension in the string would be greatest when the stone is

in the highest position

in the lowest position

in a position when it is horizontal

tension remains same in all the positions

A ball weighing 0.14 kg is being whirled in a horizontal circle at the end of a string 0.5 m long. If the breaking tension of the string is 35 N, the maximum angular velocity with which the stone can be whirled is approximately___________

12.9 rad/s

15.8 rad/s

22.4 rad/s

31.6 rad/s

A body of mass 1 kg is attached to a string 1 m long and is whirled in a horizontal circle. If the string ca withstand a tension of 25 N, the maximum whirling speed can be

5 m/s

6.8 m/s

9.5 m/s

12.5 m/s

The rotational analogue of force in linear motion is

couple

torque

moment of momentum

moment of inertia

A zero torque acting on a system will result in conversation of

linear velocity

angular velocity

angular momentum

moment of momentum

An attempt to turn a key into a lock manifests in the application of

coplanar force

moment

couple

torque

Mark the wrong statement

The constituent particles of a rigid body retain their relative positions even in motion

Torque is necessary to change the angular velocity of a rotating body

In the absence of an external torque, the angular velocity of the system is conserved

Moment of inertia is the analogue of mass in linear motion

Paper has 32 questions which have to be completed in an hours time approximately.

an attempt to turn a key into a lock manifests in the application of

27 days 1 hours 42 minutes ago

an attempt to turn a key into a lock manifests in the application of

368 days 5 hours 55 minutes ago

an attempt to turn a key into a lock manifests in the application of

368 days 5 hours 57 minutes ago

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