Kinematics Question 527
Question: Two cars of masses $ {m _{1}}andm _{2} $ are moving in circles of radii $ {r _{1}}andr _{2} $ , respectively. Their speeds are such tha they make complete circles in the same time t. The ratic of their centripetal acceleration is
Options:
A) $ m _{1}r _{1}:m _{2}r _{2} $
B) $ m _{1}:m _{2} $
C) $ r _{1}:r _{2} $
D) $ 1:1 $
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Answer:
Correct Answer: C
Solution:
[c] Centripetal acceleration, $ a _{e}={{\omega }^{2}}r $
Angular velocity, $ \omega =\frac{2\pi }{T} $ The cars make complete circle in same time.
As $ T _{1}=T _{2}\Rightarrow {\omega _{1}}={\omega _{2}} $
$ \therefore \frac{{a _{c _{1}}}}{{a _{c _{2}}}}=\frac{r _{1}}{r _{2}} $
