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An aeroplane executes a horizontal loop at a speed of \( 720 \mathrm{kmph} \) with its wings banked at \( 45^{\circ} \).
What is the radius of the loop? Take \( \mathrm{g}=10 \mathrm{~ms}^{-2} \).

A 4
B \( 4.5 \mathrm{~km} \)
C \( 7.2 \mathrm{~km} \)
D \( 2 \mathrm{~km} \)

Verified Solution

Answer & Solution

Correct Answer

(A) 4

Step-by-step Solution

Detailed explanation

Given, speed of aeroplane \(=720 \mathrm{kmph}=200 \mathrm{~ms}^{-1}\)
angle of wings \(=45^{\circ} ; g=10 \mathrm{~ms}^{-2}\)
Now we know that
\(\tan \theta=\frac{v^{2}}{r g} \Rightarrow r=\frac{v^{2}}{\tan \theta \times g}\)
\(\Rightarrow r=\frac{(200)^{2}}{\tan 45^{\circ} \times 10}=\frac{(200)^{2}}{10}=400 \mathrm{~m}=4 \mathrm{~km}\)
Thus, radius of the loop is \(4 \mathrm{~km}\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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An aeroplane executes a horizontal loop at a speed of \( 720 \mathrm{kmph} \) with its wings banked at \( 45^{\circ} \).What is the radius of the loop? Take \( \mathrm{g}=10 \mathrm{~ms}^{-2} \).

Step-by-step Solution

An aeroplane executes a horizontal loop at a speed of \( 720 \mathrm{kmph} \) with its wings banked at \( 45^{\circ} \).
What is the radius of the loop? Take \( \mathrm{g}=10 \mathrm{~ms}^{-2} \).