A body performing uniform circular motion of radius ' $R$ ' has frequency ' $n$ '. Its centripetal…
A body performing uniform circular motion of radius ' $R$ ' has frequency ' $n$ '. Its centripetal acceleration per unit radius is proportional to $(n)^x$. The value of $x$ is
1
2
-1
-2
Solution
Centripetal acceleration is given by,
$\begin{aligned}
& \mathrm{a}_{\mathrm{c}}=\omega^2 \mathrm{R} \\
& \frac{\mathrm{a}_{\mathrm{c}}}{\mathrm{R}}=(2 \pi \mathrm{n})^2 \\
& \frac{\mathrm{a}_{\mathrm{c}}}{\mathrm{R}}=4 \pi^2 \mathrm{n}^2
\end{aligned}$ Comparing the above result with $(\mathrm{n})^{\mathrm{x}}$
$x=2$