Question

What is approximately the centripetal acceleration (in units of acceleration due to gravity on earth, g = 10 ${ms}^{- 2}$ ) of an aircraft flying at a speed of 400 ${ms}^{- 1}$ through a circular arc of radius 0.6 km?

Difficult

Solution

Here, v = 400 ${ms}^{- 1}$
r = 0.6 km = 0.6 $\times 10^{3} m$
g = 10 ${ms}^{- 2}$
Centripetal acceleration,
$a_{c} = \frac{v^{2}}{r} = \frac{{(400 {ms}^{- 1})}^{2}}{0.6 \times 10^{3} m}$
= $\frac{16 \times 10^{4} m^{2} s^{- 2}}{0.6 \times 10^{3} m} = \frac{16 \times 10}{0.6} {ms}^{- 2}$
= 26.7 $\times 10 {ms}^{- 2}$
In the units of g ( = 10 ${ms}^{- 2}$ ), the centripetal acceleration is 26.7

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