A particle is performing uniform circular motion along the circumference of the circle of diameter 1 m with…
A particle is performing uniform circular motion along the circumference of the circle of diameter 1 m with frequency 4 Hz . The acceleration of the particle in $\mathrm{m} / \mathrm{s}^2$ is
$8 \pi^2$
$16 \pi^2$
$24 \pi^2$
$32 \pi^2$
Solution
For a body performing U.C.M, $\mathrm{a}=\omega^2 \mathrm{x}$ and
$\begin{aligned}
& \omega=2 \pi \mathrm{f} \\
& \mathrm{x}=\frac{\mathrm{d}}{2}=.5 \mathrm{~m}
\end{aligned}$
$\begin{aligned} & a=4 \pi^2 f^2 \times .5 \Rightarrow a=4 \pi^2(4)^2 \times .5 \\ \therefore \quad & a=32 \pi^2\end{aligned}$