Question

An air craft executes a circular loop at a speed of 200 ms⁻¹ with its wings banked at 45°. The radius of the loop is (g = 10 ms⁻²) *

(a) 4 km

(b) 5 km

(c) 8 km

(d) 12 km

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Answer 1

It has given that an aircraft executes a circular loop at a speed of 200 m/s with its wings banked at 45°.

We have to find the radius of the circular loop.

solution : see the diagram as shown in figure.

Here let N is normal reaction acting on the aircraft due to banked and mg is weight of aircraft. r is the radius of circular loop.

At equilibrium,

Nsin45° = mv²/r .....(1)

And Ncos45° = mg .....(2)

From equations (1) and (2), we get,

Tan45° = mv²/rmg

⇒1 = v²/rg

⇒r = v²/g = (200 m/s)²/10 m/s² = 4000 m = 4km

Therefore the radius of circular loop is 4km