UNIFORM CIRCULAR MOTION

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UNIFORM CIRCULAR MOTION
1. What is the centripetal force needed to keep a 1.50 kg body moving in a circle of radius 1.0 m at a
speed of 2 m/s?
2. A string 1.5 m long is used to whirl a 1.5 kg stone in a vertical circle to that its velocity at the top is
6 m/s. What is the tension in the string when it is in the horizontal position? (g = 9.8 m/s 2 )
3. A boy swings a pail of water in a vertical circle of 5 m in radius. What is the minimum angular at
the top if water is not to spill?
4. A spherical cage is erected for performing a motorcycle feat of ‘going in a vertical circle’. If the
radius of the cage is 5 m, with what speed must the rider perform the feat so that he may not fall? (g
= 9.8 m/s 2 )
5. A motorcyclist is to ride upside down around a loop of radius 5 m. The mass of the motorcycle and
the rider is 200 kg.
(a) What is the force with which the motorcycle presses against at the top of the vertical circle
where the speed is 8 m/s?
(b) What is the minimum speed at the top if the motorcycle is not to fall away from the loop? (g
= 9.8 m/s 2 )
6. A phonograph turntable rotates at a constant speed of 72 revolutions per minute. It is found that a
small object placed on a record will remain at rest relative to the record if its distance from the
centre is less the 6 cm, but will slip if the distance is any greater. Find the coefficient of friction
between the object and the record.
7. A 2500 kg car is rounding a curve of radius 100 m on a level road. The maximum frictional force
the road can exert on the tyres of the car is 5000 N. What is the highest speed at which the car can
go round the curve?
8. What is the greatest speed at which a car can take a turn of radius 60 m on a road that is banked at
an angle of 15º? (g = 9.8 m/s 2 )
9. At what angle must a railway track with a bend of radius 196 m be banked for safe running of trains
at speeds not more than 9.8 m/s?
10. A sphere of mass 200 g is attached to an inextensible string of length 130 cm whose upper end is
fixed to the ceiling. The sphere is made to describe a horizontal circle of radius 50 cm.
(a) Calculate the time period of revolution.
(b) What is the tension in the string?
11. A body of mass 0.5 kg is whirled round in a vertical circle of radius 1.2 m. If the speed at the
lowest point is 8 m/s compute the maximum and minimum tension in the string.
12. A pendulum bob of mass 0.25 kg is attached to a vertical string 1 m long. The bob is now made to
revolve in a horizontal circle of radius 0.5 m. Find the period of the motion and the tension in the
string (g = 10 m/s 2 ).
13. In the figure below a simple pendulum of length ‘l’ has a bob of mass ‘m’, and it is oscillating with
angular amplitude ‘α’. Find the value of the tension at the instant the angular displacement from the
equilibrium position is ‘α’ and when it is ‘β’.

14. A body of mass 1 kg is whirled round in a vertical circle of radius 2 m by revolving a string
inclined to the vertical. If the body revolves with a speed of 2 m/s, find
(a) The tension in the string.
(b) The angle of inclination of the string to the vertical. (g = 9.8 m/s 2 )
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SUPPLEMENTARY PROBLEMS
15. A train is moving with a speed of 72 km/h on a curved railway track of 400 m radius. A spring
balance loaded with a block of mass 5 kg is suspended from the ceiling of the train. What would be
the reading of the balance?
16. A string of length 1 m is fixed at one end and carries a mass of 100 g at the other end. This string
makes 2/π revolutions per second around a vertical axis passing through its fixed end. Calculate the
vertical height by which the mass will rise if the string now makes 4/π revolutions per second.
17. A particle moves along a circle of radius 0.02 m. The relationship between the distance ‘S’ and time
3
‘t’ is given by S ct with c 10 3 m/s 3 . When the linear speed of the particle is 0.3 m/s what is
the tangential and centripetal accelerations?
Answers
1. 6 N
2. 65.4 N
3. 1.4 rad/s
4. 7.0 m/s
5. 600 N; 7.0 m/s
6. 0.347
7. 14.1 m/s
8. 12.55 m/s
9. 2.86˚
10. 2.2 s; 2.12 N
11. 31.57 N; 2.17 N
12. 1.85 s; 2.9 N
13. mg cos ;
2mg
cos cos mg cos
14. 10.2 N; 11˚
15. 49.2 N
16. 0.47 m
17. 0.06 m/s 2 ; 4.5 m/s 2