Two bodies of masses $\mathrm{m}$ and $3 \mathrm{~m}$ are rotating in horizontal circles of radius $r$ and…

Two bodies of masses $\mathrm{m}$ and $3 \mathrm{~m}$ are rotating in horizontal circles of radius $r$ and $\frac{r}{3}$ respectively. The tangential speed of body of mass $m$ is $n$ times that of the value of heavier body. while the centripetal force is same for both. The value of $n$ is
  1. 3
  2. 9
  3. 1
  4. 6

Solution

Centripetal force is same on both, therefore: $\begin{aligned} & \frac{m(n v)^2}{r}=\frac{3 m v^2}{\left(\frac{r}{3}\right)} \\ & \Rightarrow n^2=9 \\ & \Rightarrow n=3\end{aligned}$

Asked in: MHT CET 2022 (10 Aug Shift 2)

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