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 $m _1=m _2$ 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
$F _1=F _2$
$\frac{m _1 v _1^{2}}{r _1}=\frac{m _2 v _2^{2}}{r _2}$ $\Rightarrow \frac{v _1}{v _2}=\sqrt{\frac{r _1}{r _2}}=\frac{\sqrt{3}}{2}$
