A particle of mass m hangs from a ceiling by a string of length L and moves in a horizontal circle of radius r, where r = L/sqrt(2). Find the speed of the particle.

sqrt(rg)
sqrt(2rg)
2 sqrt(rg)
sqrt(rg/2)

Correct answer: sqrt(rg)

Solution

With r = L/sqrt(2), the string makes 45 deg with the vertical, so tan(theta) = 1 and v² = r g tan(theta) = r g, giving v = sqrt(rg).

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