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3-2.Motion in Plane
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A particle moves in a circle of radius $25\,cm$ at two revolutions per sec. The acceleration of the particle in $m/s^2$ is
A$\pi ^2$
B$8\pi ^2$
C$4\pi ^2$
D$2\pi ^2$
Solution
$\mathrm{r}=25 \times 10^{-2} \mathrm{m}, \mathrm{f}=2 / \mathrm{sec}$
$\therefore \quad \omega=2 \pi f=4 \pi \mathrm{rad} / \mathrm{sec}$
Acceleration $=\omega^{2} \mathrm{r}=(4 \pi)^{2} \times 25 \times 10^{-2}$
$=16 \times 25 \times 10^{-2} \pi^{2} \mathrm{m} / \mathrm{s}^{2}=4 \pi^{2} \mathrm{m} / \mathrm{s}^{2}$
$\therefore \quad \omega=2 \pi f=4 \pi \mathrm{rad} / \mathrm{sec}$
Acceleration $=\omega^{2} \mathrm{r}=(4 \pi)^{2} \times 25 \times 10^{-2}$
$=16 \times 25 \times 10^{-2} \pi^{2} \mathrm{m} / \mathrm{s}^{2}=4 \pi^{2} \mathrm{m} / \mathrm{s}^{2}$
Standard 11
Physics
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