Question

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

• A. 4
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

2

Answer 2

Let v be the tangential speed of the heavier stone. Then, the centripetal force experienced by lighter stone is $(F_c)_{lighter}=\frac{m(nv)^2}{r}$
and that of heavier stone is $(F_c)_{heavier}=\frac{2mv^2}{(r/2)}$

But it is given that (Fc)lighter = (Fc)heavier

$\therefore$ $\frac{m(nv)^2}{r} = \frac{2mv^2}{(r/2)}$

$n^2\Bigg(\frac{mv^2}{r}\Bigg)=4\Bigg(\frac{mv^2}{r}\Bigg)$

n2 = 4

n = 2