A person walks one lap along a circle at a speed \(v\). Thereafter, he runs one lap along the boundary of the largest square that can be inscribed in the circle at a speed \(3v\). The ratio of the…
Question and options
A person walks one lap along a circle at a speed . Thereafter, he runs one lap along the boundary of the largest square that can be inscribed in the circle at a speed . The ratio of the time he walks to the time he runs is
Answer and explanation
Correct answer: D - \(\frac{3\pi}{2\sqrt{2}}\)
Walk time = 2*pi*r/v. Largest inscribed square has side r*sqrt2, perimeter 4 sqrt2 r, run time = 4 sqrt2 r/(3v). Ratio = 2 pi * 3/(4 sqrt2) = 3 pi/(2 sqrt2).
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