Motion In Two Dimensions Question 2
Question 2 - 2024 (29 Jan Shift 1)
If the radius of curvature of the path of two particles of same mass are in the ratio $3: 4$, then in order to have constant centripetal force, their velocities will be in the ratio of:
(1) $\sqrt{3}: 2$
(2) $1: \sqrt{3}$
(3) $\sqrt{3}: 1$
(4) $2: \sqrt{3}$
Show Answer
Answer: (1)
Solution:
Given $\mathrm{m}{1}=\mathrm{m}{2}$ and $\frac{r_{1}}{r_{2}}=\frac{3}{4}$
As centripetal force $F=\frac{m^{2}}{r}$
In order to have constant (same in this question) centripetal force
$\mathrm{F}{1}=\mathrm{F}{2}$
$\frac{\mathrm{m}{1} \mathrm{v}{1}^{2}}{\mathrm{r}{1}}=\frac{\mathrm{m}{2} \mathrm{v}{2}^{2}}{\mathrm{r}{2}}$ $\Rightarrow \frac{\mathrm{v}{1}}{\mathrm{v}{2}}=\sqrt{\frac{\mathrm{r}{1}}{\mathrm{r}{2}}}=\frac{\sqrt{3}}{2}$
