Kinematics Question 789
Question: If the radius of curvature of the path of two particles of same masses are in the ratio 1 : 2, then in order to have constant centripetal force, their velocity, should be in the ratio of [Pb. PET 2000]
Options:
A) 1 : 4
B) 4 : 1
C) $ \sqrt{2}:1 $
D) $ 1:\sqrt{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
The centripetal force, $ F=\frac{mv^{2}}{r} $
therefore $ r=\frac{mv^{2}}{F} $
$ r\propto v^{2} $ or $ v\propto \sqrt{r} $
(If m and F are constant), therefore $ \frac{v _{1}}{v _{2}}=\sqrt{\frac{r _{1}}{r _{2}}}=\sqrt{\frac{1}{2}} $
