Question

Two stones of masses $m$ and $2m$ 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

• A. 4
• B. 1
• C. 2
• D. 3

Answer 1

Answer: (C)

Let $v$ be tangential speed of heavier stone.
Then, centripetal force experienced by lighter stone is ${\left(F_c\right)}_{\text{lighter }}=\frac{m(nv{)}^2}{r}$
and that of heavier stone is
${\left(F_c\right)}_{\text{heavier }}=\frac{2m{v}^2}{(r/2)}$
But ${\left(F_c\right)}_{\text{lighter }}={\left(F_c\right)}_{\text{heavier }}$ (given)
$\therefore \frac{m(nv{)}^2}{r}=\frac{2m{v}^2}{(r/2)}$
$n^2\left(\frac{m{v}^2}{r}\right)=4\left(\frac{m{v}^2}{r}\right)$
$n^2=4$ or $n=2$