Question

A particle moves in a circle of radius $25\text{cm}$ at two revolutions per second. The acceleration of the particle in $m/s^2$ is:

• A. ${\pi }^2$
• B. $8{\pi }^2$
• C. $4{\pi }^2$
• D. $2{\pi }^2$

Answer 1

Answer: (C)

$4{\pi }^2$

Here $T=\frac{1}{2}\text{sec}$ the required centripetal acceleration for moving in a circle is

${\text{a}}_{\text{c}}=\frac{{\text{v}}^2}{\text{r}}=\frac{(\text{r}\omega {)}^2}{\text{r}}=\text{r}{\omega }^2=\text{r}\times (2\pi /\text{T}{)}^2$

So ${\text{a}}_{\text{c}}=0.25\times (2\pi /0.5{)}^2$

$=16{\pi }^2\times .25=4.0{\pi }^2$