Question

An aeroplane flying at constant speed $105m/s$ towards East, makes a gradual turn following a circular path to fly South. The turn takes $15$ seconds to complete. The magnitude of the centripetal acceleration during the turn is

• A. $\frac{7\pi }{2}m/s^2$
• B. $\frac{46\pi }{3}m/s^2$
• C. $\frac{23\pi }{6}m/s^2$
• D. $14\pi m/s^2$

Answer 1

The correct option is A $\frac{7\pi }{2}m/s^2$

For $1/4$ cycle it takes $15sec$.
Therefore, time period$T=60s$.
We have,
$T=\frac{2\pi }{\omega }=\frac{2\pi r}{V}$
or
$V=\frac{2\pi r}{T}$
Thus, we get the centripetal acceleration as $\frac{V^2}{r}=\frac{2\pi V}{T}=7\pi /2m/s^2$