Question

Two stones of masses $m$ and $2m$ are whirled in horizontal circles. The heavier one is whirled in a circle of radius $\frac{r}{2}$ and the lighter one in a circle of radius $r$. The tangential speed of lighter stone is $n$ times that of the speed of heavier stone. If they experience the same centripetal forces, the value of $n$ is

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Centripetal force is same on both as given.
So
$\Rightarrow \frac{m(n{v}_2{)}^2}{r}=\frac{2m{v}_2^2}{\frac{r}{2}}$
$\Rightarrow n^2=4$
$\Rightarrow n=2$