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Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in radius r and the lighter one in radius r/2. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is:

1. 3
2. 4
3. 1
4. 2

Correct answer: 4

Solution

The centripetal force is given by F = mv²/r. For the heavier stone, F = (2m)(v₁²)/r, and for the lighter stone, F = (m)(v₂²)/(r/2). Equating the forces, (2m)(v₁²)/r = (m)(v₂²)/(r/2). Simplifying, v₂² = 4v₁², so v₂ = 2v₁. Thus, n = 2.

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