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

m_{1} r_{1}

m_{2} r_{2}

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m_{1}

m_{2}

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r_{1}

r_{2}

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1 : 1

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Solution

The correct option is C $r_{1}$ : $r_{2}$
Since both make complete circles in same time 't'. so angular velocity is also same for both the masses.
since centripetal acceleration $a = ω^{2} r$
so $\frac{a_{1}}{a_{2}} = \frac{{ω_{1}}^{2} r_{1}}{{ω_{2}}^{2} r_{2}}$
and $ω_{1} = ω_{2}$
so $\frac{a_{1}}{a_{2}} = \frac{r_{1}}{r_{2}}$

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