An aircraft executes a horizontal loop of ...

Motion in a Plane

Question : 18 of 32

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An aircraft executes a horizontal loop of radius 1.00 km with a steady speed of 900 km h

^{-1}

. Compare its centripetal acceleration with the acceleration due to gravity.

Solution:

Here,

r = 1\,\text{km} = 1000\,\text{m};

v = 900\,\text{km}\,\text{h}^{-1} = 900 \times \frac{1000}{3600}\,\text{m}\,\text{s}^{-1}

= 250\,\text{m}\,\text{s}^{-1}

The centripetal acceleration of the aircraft is given by

a = \frac{v^{2}}{r} = \frac{(250)^{2}}{1000}

= \frac{62500}{1000} = 62.5\,\text{m}\,\text{s}^{-2}

Acceleration due to gravity,

g = 9.8\,\text{m}\,\text{s}^{-2}

\therefore \frac{\text{Centripetal acceleration}}{\text{Acceleration due to gravity}} = \frac{a}{g} = \frac{62.5}{9.8}

\frac{a}{g} = 6.4

a = 6.4 g

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