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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 \( \mathrm{g}=10 \mathrm{~ms}^{-2} \).
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What is the radius of the loop? Take \( \mathrm{g}=10 \mathrm{~ms}^{-2} \).
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The correct answer is:
4
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 $4 \mathrm{~km}$
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 $4 \mathrm{~km}$
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