Uncategorized: Practice Problem & Solution
Two stones of masses (m) and (2m) are whirled in horizontal circles, the heavier one in a radius (r/2) and the lighter one in radius (r). 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: (2015 Re)
Solution Explained:
To solve this problem, we apply the core principles of Uncategorized. Understanding the underlying formula is key to arriving at the correct answer below:
Centripetal force (F_c = frac{mv^2}{r}). Given (F_{c1} = F_{c2}). So (frac{(2m)v_1^2}{(r/2)} = frac{m v_2^2}{r}). This simplifies to (frac{4mv_1^2}{r} = frac{mv_2^2}{r}), which gives (v_2^2 = 4v_1^2), so (v_2 = 2v_1). Therefore, (n=2).
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