Question

Two particles of masses $m$ and $\frac{m}{2}$ are moving along the circular paths of radii $r$and $3r,$ respectively, with equal speed. What is the ratio of their accelerations?

• A. $1:1$
• B. $1:3$
• C. $3:1$
• D. $2:1$

Answer 1

The correct option is C

$3:1$

Step 1: Given data and formula used

Given:

Mass m particle moving in the circular orbital of radius $r$

A mass $\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ particle moving in the circular orbital of radius $3r$

Both have equal velocity $v$

The formula of centripetal acceleration$\left(a\right)=\frac{v^2}{r}$

Step 2: Calculation of ratio of acceleration

$$\begin{gathered} {\mathrm{a}}_1=\frac{{\mathrm{v}}^2}{\mathrm{r}},{\mathrm{a}}_2=\frac{{\mathrm{v}}^2}{3\mathrm{r}} \\ \frac{{\mathrm{a}}_1}{{\mathrm{a}}_2}=\frac{{\displaystyle \frac{{\mathrm{v}}^2}{\mathrm{r}}}}{{\displaystyle \frac{{\mathrm{v}}^2}{3\mathrm{r}}}}=\frac{3}{1} \end{gathered}$$

Thus, the ratio is 3:1

Hence, the correct option is (c).