Unit – II E

Problems in Circular Motion:

Different systems and corresponding agencies providing centripetal forces.

Centripetal Acceleration 18

Formulae

Centripetal Acceleration 19

Conversions

Centripetal Acceleration 20

  1. To simulate the acceleration of high speed fighter plane, astronauts are spun at the end of a long rotating beam of radius 5 m. Find the angular velocity required to generate a centripetal acceleration 3 times the acceleration due to gravity.
  2. To simulate the acceleration of large rockets, astronauts are spun at the end of a long rotating beam of radius 9.8 m. Find the angular velocity required to generate a centripetal acceleration 8 times the acceleration due to gravity.
  3. A 0.5 kg. mass is rotated in a horizontal circle of radius 20 cm. Calculate the centripetal force acting on it, if its angular speed of revolution is 0.8 rad /s.
  4. An object of mass 0.5 kg is whirled in a horizontal circle of radius 20 cm. Calculate centripetal force acting on it, if its angular speed of revolution is 0.6 rad/s.
  5. A one kg mass tied at the end of the string 0. 5 m long is whirled in a horizontal circle, the other end of the string being fixed. The breaking tension in the string is 50 N. Find the greatest speed that can be given to the mass.
  6. An object of mass 0.5 kg is whirled in a horizontal circle of radius 20 cm. Calculate the maximum number of revolution per minute, so that the string does not break. Breaking tension of string is 9.86 N.
  7. A body of mass 1 kg is tied to a string and revolved in a horizontal circle of radius 1 m. Calculate the maximum number of revolution per minute, so that the string does not break. Breaking tension of string is 9.86 N.
  8. A 2 kg mass is tied to a string at one end and rotated in a horizontal circle of radius 0.8 m about the other end. If the breaking tension in the string is 250 N, find the maximum speed at which mass can be rotated.
  9. A stone is tied to a string 50 cm long and rotated uniformly in a horizontal circle about the other end. If the string can support a maximum tension ten times the weight of the stone, find the maximum number of revolutions per second the string can make before it breaks.
  10. A certain string breaks under a tension of 45 kg-wt. A mass of 100 g is attached to one end of a piece of this string 500 cm long and rotated in a horizontal circle. Neglecting the effect of gravity, find the greatest number of revolutions which the sting can make without breaking.
  11. A spherical body of mass 1 kg and diameter 2 cm rotates in a horizontal circle at the end of a string 1.99 m. long. What is the tension in the string when the speed of rotation is 6 revolutions in 1.5 s?
  12. A mass of 5 kg is tied at the end of the string 1.2 m long rotates in a horizontal circle. If the breaking tension in the string is 300 N , find the maximum number of rotations per minute the mass can make.
  13. The breaking tension of a string is 80 kg.-wt. A mass of 1 kg is attached to the string and rotated in a horizontal circle on a horizontal surface of radius 2 m. Find the maximum number of revolutions made without breaking.
  14. A string breaks under a tension of 10 kg-wt. If a string is used to revolve a body of mass 1.2 gm in a horizontal circle of radius 50 cm, what is the maximum speed with which a body can be revolved? When a body is revolving at maximum speed, what is its period ? (g = 9.8 m/s2)
  15. A body of mass 2 Kg is tied to the end of a string of length 1.5 m and revolved about the other end (kept fixed) in a horizontal circle. If it makes 300 rev/min, calculate the linear velocity, the acceleration and the force acting upon the body.
  16. A body of mass 20 g rests on a smooth horizontal plane. The body is tied by a light inextensible string 80 cm long to a fixed point in the plane. Find the tension in the string if the body is rotated in a circular path at 30 rev/min. What is the force experienced by the fixed point?
  17. How fast should the earth rotate about it axis so that the apparent weight of a body at the equator be zero? How long would a day be then ? Take the radius of the earth = 6400 km.
  18. An electron of mass 9 x 10-34 kg is revolving in a stable orbit of radius 5.37 x 10-14 m. If electrostatic force of attraction between electron and proton is 8 x 10-8 N. Find the velocity of electron.
  19. A bucket containing water is tied to one end of a rope 8 m long and rotated about the other end in a vertical circle. Find the minimum number of rotations per minute in order that water in the bucket may not spill ?
  20. The vertical section of a road over a bridge in the direction of its length is in the form of an arc of a circle of radius 19.5 m. Find the greatest velocity at which a car can cross the bridge without losing contact with the road at the highest point if the c.g. of the car is 0.5 m from the ground.
  21. A flyover bridge is in the form of a circular arc of radius 30 m. Find the limiting speed at which a car can cross the bridge without losing contact with the road at the highest point. Assume the centre of gravity of the car to be 0.5 in above the road.
  22. A motor cyclist rides in a vertical circle in a hollow sphere of radius 3 m. Find the minimum speed required so that he does not lose contact with the sphere at the highest point. Also find its angular speed.
  23. An object of mass 100 g move around circumference of circle of radius 2m with constant anguar speed of 7.5 rad/s. Compute its linear speed and force directed towards centre.
  24. A car of mass 2000 kg rounds a curve of radius 250 m at 90 km/hr. Compute its angular speed, centripetal acceleration and centrifugal force.
  25. A bucket containing water is tied to one end of a rope 0.75 m long and rotated about the other end in a vertical circle. Find the speed in order that water in the bucket may not spill ? Also find the angular speed. (g = 9.8 m/s2)
  26. A 0.5 kg mass is tied to one end of a string and rotated in a horizontal circle of 1.25 m radius about the other end. What is the tension in the string if the period of revolution is 5 s. What is the naximum speed of rotation and the corresponding period if the string can withstand a maximum tension of 150 N.
  27. A motor cyclist rides in a vrtical circle in a hollow sphere of radius 12.8 m. Find the minimum speed required so that he does not lose contact with the sphere at the highest point.
  28. A spherical bob of diameter 3 cm having a mass 100 g is attached to the end of a string of length 48.5 cm. Find the angular velocity and the tension in the string, if the bob is rotated at a speed of 600 r.p.m. in a horizontal circle.

Answers:

  1. 2.425 rad/s
  2. 2.828 rad/s
  3. 0.064 N
  4. 0.036 N
  5. 5 m/s
  6. 94.82 r.p.m.
  7. 30 r.p.m.
  8. 10 m/s
  9. 2.23 per second
  10. 4.73 rev/s
  11. 1262 N
  12. 67.5 r.p.m.
  13. 3.152 r.p.s.
  14. 202.1 m/s, 0.016 s
  15. 47.1 m/s; 1479 m/s2 ; 2958 N
  16. 0158 N; same
  17. 1.237x 10-3 rad/s; 5077s
  18. 2.185 x 106 m/s
  19. 94.87 r.p.m
  20. 14 m/s
  21. 17.3 m/s
  22. 5.42 m/s, 1.807 rad/s
  23. 15 m/s, 11.25 N
  24. 0.1 rad/s, 2.5 m/s2, 5000 N
  25. 2.711 m/s, 3.615 rad/s
  26. 0.986 N, 19.36 m/s, 0.45 s
  27. 11.2 m/s
  28. 62.84 rad/s, 197.2 N

Solutions of above problems will be uploaded soon on this page

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