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A particle is moving along the circular path with constant speed and centripetal acceleration ' $a$ '. If the speed is doubled, the ratio of its acceleration after and before the change is
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Verified Answer
The correct answer is:
4:1
Centripetal acceleration is given by
$\begin{aligned}
& \mathrm{a}=\frac{\mathrm{v}^2}{\mathrm{r}} \therefore \mathrm{a} \propto \mathrm{v}^2 \\
& \therefore \frac{\mathrm{a}_2}{\mathrm{a}_1}=\left(\frac{\mathrm{v}_2}{\mathrm{v}_1}\right)^2=(2)^2=4
\end{aligned}$
$\begin{aligned}
& \mathrm{a}=\frac{\mathrm{v}^2}{\mathrm{r}} \therefore \mathrm{a} \propto \mathrm{v}^2 \\
& \therefore \frac{\mathrm{a}_2}{\mathrm{a}_1}=\left(\frac{\mathrm{v}_2}{\mathrm{v}_1}\right)^2=(2)^2=4
\end{aligned}$
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