Question 273: Work, Energy and Power & Circular Motion

Question

Two bodies of masses '$$\mathrm{m}$$' and '$$3 \mathrm{~m}$$' are rotating in horizontal speed of the 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

Accepted Answer

For body A, mass $$=\mathrm{m}$$, radius of the circle $$=\mathrm{r}$$
For body B, mass $$=3 \mathrm{~m}$$ and radius of the circle $$=\frac{r}{3}$$ and $$\mathrm{v}$$ and $$\mathrm{v}$$' are the tangential speeds
$$	ext { For A, C.P. force }=\frac{\mathrm{mv}^2}{\mathrm{r}}\quad 	ext{.... (1)}$$
For B, C.P. force $$=\frac{3 \mathrm{~m} \cdot \mathrm{v}^{\prime 2}}{\mathrm{r} / 3}=\frac{9 \mathrm{mv}^{\prime 2}}{\mathrm{r}}\quad 	ext{.... (2)}$$
and it is given that $$\mathrm{v}=\mathrm{nv}{ }^{\prime}$$
Since the C.P. force is same for both
$$\begin{aligned}
& 	herefore \frac{\mathrm{mv}^2}{\mathrm{r}}=\frac{9 m v^{\prime 2}}{\mathrm{r}} \
& 	herefore \mathrm{v}^2=9 \mathrm{v}^{\prime 2} 	ext { but } \mathrm{v}=\mathrm{nv^{ \prime }} \
& 	herefore \mathrm{n}^2 \mathrm{v}^{\prime 2}=9 \mathrm{v}^{\prime 2} \
& 	herefore \mathrm{n}^2=9 \quad 	herefore \mathrm{n}=3
\end{aligned}$$

Answer

3

Answer

1

Answer

9

Answer

6

Work, Energy and Power & Circular Motion

Two bodies of masses '$\mathrm{m}' and '3 \mathrm{~m}' are rotating in horizontal speed of the body of mass 'm' is n times that of the value of heavier body; while the centripetal force is same for both. The value of n$ is

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