If an aeroplane is rotating in a circle of radius $1 k m$ , making an angle $45^{o}$ with the horizontal, find the speed at which it is moving. [assume $g = 10 m / s^{2}$ ]

10 m / s

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100 m / s

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300 m / s

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200 m / s

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Solution

The correct option is B $100 m / s$
We know that the angle through which the aeroplane should bend is given by $θ = t a n^{- 1} (\frac{v^{2}}{R g})$
Substituting the given values we get $45^{o} = t a n^{- 1} (\frac{v^{2}}{1000 \times 10})$
$\Rightarrow$ $10000 = v^{2}$
$\Rightarrow$ $v = 100 m / s$

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