Question

# Two cars of masses $$\mathrm{m}_{1}$$ and $$\mathrm{m}_{2}$$ are moving in circles of radii $$\mathrm{r}_{1}$$ and $$\mathrm{r}_{2}$$ respectively. Their speeds are such that they make complete circles in the same time $${t}$$. The ratio of their centripetal acceleration is :

A
m1r1 : m2r2
B
m1 : m2
C
r1 : r2
D
1 : 1

Solution

## The correct option is C $$\mathrm{r}_{1}$$ : $$\mathrm{r}_{2}$$Since both make complete circles in same time 't'. so angular velocity is also same for both the masses. since centripetal acceleration $$a={ \omega }^{ 2 }r$$so $$\dfrac { { a }_{ 1 } }{ { a }_{ 2 } } =\dfrac { { { \omega }_{ 1 } }^{ 2 }{ r }_{ 1 } }{ { { \omega }_{ 2 } }^{ 2 }{ r }_{ 2 } }$$and $${ \omega }_{ 1 }={ \omega }_{ 2 }$$so $$\dfrac { { a }_{ 1 } }{ { a }_{ 2 } } =\dfrac { { r }_{ 1 } }{ { r }_{ 2 } }$$Physics

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