Two stones of masses m and $$2$$ m are whirled in horizontal circles, the heavier one in a radius $$r2$$ 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

Question

Two stones of masses m and $$2$$ m are whirled in horizontal circles, the heavier one in a radius $$r2$$ 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

Infinity Learn · Accepted Answer

Let ν be tangential speed of heavier stone. Then, Centripetal force experienced by lighter stone isFclighter $$=m(nv)2rand$$ that of heavier stone is Fcheavier $$=2mv2(r/2)$$ But Fclighter $$=Fcheavier$$    (given) ∴  $$m(nv)2r=2mv2(r/2)n2mv2r=4mv2rn2=4$$ or $$n=2$$

Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ 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

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Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius r2 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

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Two stones of masses m and 2 m are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ 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