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 $

Show Answer

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}} $



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