Question

A particle moves in a circle of radius $1\text{m}$ with a uniform speed, it completes one revolution in $2\pi \text{seconds}$, the acceleration of the particle is

• A. $4{\pi }^2{\text{m/s}}^2$
• B. $0.5{\text{m/s}}^2$
• C. $1{\text{m/s}}^2$
• D. $16{\pi }^4{\text{m/s}}^2$

Answer 1

The correct option is C $1{\text{m/s}}^2$

Given that the radius of circle
$\left(r\right)=1\text{m}$

Time period $\left(T\right)=2\pi \text{seconds}$

Centripetal acceleration $\left(a_c\right)=r{\omega }^2$
Since, $\omega =\frac{2\pi }{T}$

$a_c=r{\left(\frac{2\pi }{T}\right)}^2=T\times {\left(\frac{2\pi }{2\pi }\right)}^2=1{\text{m/s}}^2$
The tangential accleration $a_t=0$, as the particle moves with uniform speed.
Hence the only acceleration is $a_c=1{\text{m/s}}^2$.

Hence option C is the correct answer.