## Unit – II E |

## Problems in Circular Motion:

### Different systems and corresponding agencies providing centripetal forces.

### Formulae

### Conversions

- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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?
- 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.
- 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.
- 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)
- 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.
- 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?
- 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.
- 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. - 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 ?
- 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.
- 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.
- 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.
- 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.
- 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.
- 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)
- 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.
- 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.
- 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:

- 2.425 rad/s
- 2.828 rad/s
- 0.064 N
- 0.036 N
- 5 m/s
- 94.82 r.p.m.
- 30 r.p.m.
- 10 m/s
- 2.23 per second
- 4.73 rev/s
- 1262 N
- 67.5 r.p.m.
- 3.152 r.p.s.
- 202.1 m/s, 0.016 s
- 47.1 m/s; 1479 m/s2 ; 2958 N
- 0158 N; same
- 1.237x 10
^{-3}rad/s; 5077s - 2.185 x 10
^{6}m/s - 94.87 r.p.m
- 14 m/s
- 17.3 m/s
- 5.42 m/s, 1.807 rad/s
- 15 m/s, 11.25 N
- 0.1 rad/s, 2.5 m/s2, 5000 N
- 2.711 m/s, 3.615 rad/s
- 0.986 N, 19.36 m/s, 0.45 s
- 11.2 m/s
- 62.84 rad/s, 197.2 N

Please update the solutions from question no. 22

Please update the solution Qn. 24