Question

Two stones of masses $m$ and $2m$ are whirled in horizontal circles, the heavier one in a radius $\frac{r}{2}$ and 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. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Since, centripetal force is same:

$\frac{m_1{v}_1^2}{r_1}=\frac{m_2{v}_2^2}{r_2}$

where $m_1,v_1$ and $r_1$ belong to lighter mass and $m_2,v_2$ and $r_2$ belong to heavier mass.

$⟹\frac{m{n}^2{v}_2^2}{r}=2\frac{m{v}_2^2}{r}\times 2$

$⟹n^2=2\times 2$

$⟹n^2=4$

$⟹n=2$