What is the least speed at which an aeroplane can execute a vertical loop of 1 km radius so that there will be no tendency for the pilot to fall down at the highest point? (Ans: 99 m s⁻¹)



Data Given:



Radius of the loop = r = 1 km = 1000 m

Value of g = 9.81 m s⁻²


To Find:


Least speed of aeroplane  = v = ?


Solution:


By using formula for speed moving in orbit

v = `\sqrt {gr}`

By putting values

v = `\sqrt {9.81 m s⁻² ｘ 1000 m}`

v = `\sqrt {9810 m² s⁻² }`

v = 99.045 m s⁻¹

or

v = 99 m s⁻¹ -----------Ans.

Hence the speed of aeroplane is 99 m s⁻¹ 




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