## Unit – VC |

## Problems Motion in Vertical Circle:

### Formulae

- A stone weighing 1 kg is whirled in a vertical circle at the end of a rope of length 0.5 m. Find the velocity of a stone at a) lowest position b) midway when string is horizontal c) top most position to just complete the circle.
- A stone weighing 1 kg is whirled in a vertical circle at the end of a rope of length 0.5 m. Find the tension in the string at a) lowest position b) midway when string is horizontal c) top most position to just complete the circle.
- A stone weighing 50 g is whirled in a vertical circle at the end of a rope of length 1.8 m. Find the tension in the string and velocity of the stone at a) lowest position b) midway when string is horizontal c) top most position to just complete the circle.
- A stone weighing 1 kg is whirled in a vertical circle at the end of a rope of length 1 m. Find the tension in the string and velocity of the stone at a) lowest position b) midway when string is horizontal c) top most position to just complete the circle.
- A pilot of mass 75 kg in a jet aircraft while executing a loop the loop with a constant speed of 360 km/h.. If the radius of circle is 200, compute the force exerted by sent on the pilot a) at the top of loop b) at the bottom loop.
- A pilot of mass 50 kg in a jet aircraft while executing a loop the loop with a constant speed of 250 m/s. If the radius of circle is 5 km, compute the force exerted by sent on the pilot a) at the top of loop b) at the bottom loop.
- A ball is released from a height h along the slope and at the end of a slope moves along a circular track of radius R without falling vertically downwards. Determine the height h in terms of R.
- A 3 kg ball is swung in a vertical circle at the end of inextensible string 3 m long. What is the maximum and minimum tension in the string if the ball moves 90/p revolutions per minute.
- A 2 kg ball is swung in a vertical circle at the end of inextensible string 2 m long. What is the the speed and angular speed of the ball if the string can sustain maximum tension of 119.6 N.

### Answers

- 4.95 m/s, 3.83 m/s, 2.21 m/s
- 58.8 N, 0 N, 29,4 N
- 2.94 N, 0 N, 1.47 N
- 7 m/s, 5.42 m/s, 3.13 m/s, 58.8 N, 0 N, 29,4 N
- 3015 N, 4485 N
- 135 N, 1115 N
- h = 5R/2
- 110.4 N, 51.6 N
- 10 m/s, 5 rad/s

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